I know that a a planet or moon's rotation will slow down or speed up until it is tidally locked with a body, is Pluto's rotation being affected by the sun or is it being forced by Charon just to to be tidally locked with Charon?
Short answer. Pluto's rotation is 100% governed by Charon, or, more accurately, the Pluto-Charon system. The sun is irrelevant to it's rotation.
Small point to add. Pluto's rotation is pretty much governed by the Pluto-Charon orbit. If Charon moves closer to Pluto, Pluto's rotation will correspondingly increase. If Charon moves further away, Pluto's rotation will decrease. That's how tidal locking works. I answered the question in regards to the orbit changing, not the rotation changing, but in a tidally locked system the rotation period follows the orbital period.
I know that a a planet or moon's rotation will slow down or speed up until it is tidally locked with a body,
Tidal locking doesn't always happen. For distant orbits the tidal force that makes tidal locking happen is often very weak and very slow, often requiring more time than the lifespan of the star in that solar system.
Also, for high eccentricity orbits, classic tidal locking is impossible though resonant orbits like Mercury's 3:2 around the sun are probably fairly common. And many moons will escape their planet or crash into their planet long before mutual tidal locking occurs, though it's not uncommon for moons themselves to be tidally locked. Also small moons don't have sufficient gravity to pull the object they orbit into mutual tidal locking.
For mutual tidal locking, like Pluto-Charon, there needs to be respectible mass ratio or, perhaps an initial formation where orbital speed and rotation are very close, so it doesn't take much force to lead to mutual tidal locking. Our moon, at 1/81st the mass of the Earth, would eventually cause the Earth to tidal lock to it, but estimates say it will take longer than it will take the sun to go red-giant for that to happen, and the expected outcome of our moon is that it will crash into the Earth before there is mutual tidal locking.
So, mutual tidal locking like pluto-charon is actually pretty rare because you need the smaller object to have a significant percentage of mass to the larger one. One-way tidal locking is quite common, but your question addresses mutual tidal locking.
is Pluto's rotation being affected by the sun or is it being forced by Charon just to to be tidally locked with Charon?
For a quick approximation, the tidal force can roughly/bad approximation be estimated by the size of the object in the sky times it's density. There's other factors, ofcourse, like the size of the object receiving the tidal force, but for a rough approximation, the size in the sky gives an estimate. For example, the sun and moon each take up about 1/2 a degree of arc when viewed from the surface of the Earth, so they have similar tidal forces due to having similar size. The major difference being that the Moon is about 2.4 times more dense than the sun so it's tides are correspondingly about 2.4 times as strong.
This visual size approximation doesn't work for very-near-earth orbits, as it's the size that would appear from the center of the Earth, not the surface that should be applied.
Charon from the surface of Pluto is huge. It spans several degrees of arc, over 10 times the size the Moon appears from the Earth. The sun, from Pluto is tiny about 1/30th the size it appears from Earth, which is only about 50% larger than Venus appears in the sky at it's largest, or, about 1 minute of arc, but even at that distance the sun is still bright enough to cast visible shadows and would probably damage your retina if you stared at it. It would be the most impressive light in the sky from Pluto, but still tiny, so the tidal effect on Pluto-Charon would be quite small. (I'd prefer not to do the math, my math tends to run into errors and I'm not good with mathjax).
But the sun's tidal influence on the Pluto-Charon system is close to negligible, It can be calculated and it's not zero, but it's very small. Over a very very very long time, the Sun's tidal force will sap energy from the Pluto-Charon system and draw them closer towards each other, but at that distance, billions maybe trillions of years. Pluto is probably more likely to meet a different fate well before then, such as crashing into Neptune or being thrown out of the solar-system before the Pluto-Charon system becomes unstable.
It would be different if Pluto-Charon orbited at Mercury or Venus distance (ignoring the obvious melting of ices and outgassing in a warmer environment). That close, the sun becomes a major player in the future of the mutually tidally-locked systems, likely causing them to crash into each other, but at Pluto distance, there's virtually no effect.
When a system is mutually tidally locked with a nearly circular orbit, then it's very stable. If there's no tidal locking or one way tidal locking like Earth-Moon, then there's a tidal bulge that leads or follows the moon and that creates a force that can slow down or speed up the planet and push the moon away or draw it in closer. With tidal locking, there's no leading or following with the tidal bulge, so the orbit is less prone to change. There's always some orbital variation and some orbital energy converted to heat due to no orbits being perfectly circular, but mutual tidal locking is still a very stable orbital system with less change than most, as long as there isn't a 3rd party forcing change, such as a debris cloud creating drag or outgassing or orbiting close to a massive body that saps energy from the tidally locked orbit.
No orbits are stable forever, and considering all the factors, Pluto and Charon are close enough that they exchange some atmosphere and as the sun grows more luminous over time, that exchange will probably increase, and likely both are losing mass slowly over time due to the solar wind. This very gradual loss of mass, I would think, would cause the orbit to expand, but very slowly. With no loss of gas by the solar wind, the Pluto-Charon orbit should very slowly contract due to tidal forces from the sun and some orbital energy being converted into heat, but both of those effects are very slow. Mutual tidal locking is for the most part a very stable system.
Hope that wasn't too long, but that's the gist of it. My answer could probably be improved with some math and some linked references but that would make it even longer.
The specifics of the Pluto Charon system are complicated, so I will answer more generally for now. A single body orbiting the sun can be tidally locked with the sun if its rotational period (its day) is equal to its orbital period (its year).
The Moon is tidally locked to the Earth because the period of one orbit of the moon around the Earth takes the same amount of time as one rotation of the moon about its axis. (Note that the Earth is not tidally locked with the Moon. One Earth day does not correspond to one lunar orbit.)
A binary (dwarf) planet system (like Pluto and Charon) is considered to be tidally locked if their respective orbital periods about the common barycenter of mass are equal to their respective rotational periods, and all of these periods, for both objects, are equal to each other.
You specifically asked about the tidal effects of the Sun on Pluto. Unfortunately, the complete answer depends on the orbital parameters of Charon and Pluto's orbits around the barycenter of mass.
I will assume the orbits of Pluto and Charon are such that their orbital plane about the barycenter is not perpendicular to a radial vector drawn from the Sun to the barycenter of mass for the following explanation. (i.e. one body is slightly closer to the Sun at a given instant in the same way the Moon gets closer and farther from the Sun as it orbits the Earth).
With this assumption, tidal effects from the Sun should slow the rotation of the Pluto Charon system about the barycenter (the orbital period of each body about the barycenter of mass should decrease over time). This slowing would occur because the radially inward (toward the Sun) side of the closer body would have a greater gravitational pull on it that the farther side of that body. Thus, the Sun's gravitational pull would attempt to slow the rotational period of that body (equivalently: increase the length of that body's "day"). This process I am describing is the same as the process that caused the Moon to become tidally locked to the Earth.
The Pluto Charon system introduces complications to this explanation because of the highly inclined and atypical orbital parameters of the Pluto-Charon-[Other Plutonian Bodies] system, the varying masses of the system bodies, and the system's extreme distance from the Sun. The large orbital distance of the system from the Sun means that any tidal effects on Pluto and Charon are mild at their strongest. Thus, measurable changes due to tidal effects are next to impossible to measure over human time scales.