This was a random thought I had, and I can't seem to find any answers. I was thinking that if the Earth shrunk that could possibly cause an increase in distance from the sun resulting in earth having less gravitational pull due to the sun having less effect on it?
No, gravity is special, because it's pull is related to mass, but acceleration for a given force is inversely proportional to mass.
Galileo noticed this: he observed that two masses, one small and one heavier will fall at the same rate, if air resistance is small.
And orbiting is basically like falling around the sun.
Similarly, but on a much grander scale the orbit of a planet depends only on it's motion around the sun and not on the mass of the planet. If the Earth was magically made lighter, without changing its velocity around the sun, it would continue to move in the same way and at the same distance from the sun, just like Galileo's weights fell at the same rate.