Shooting stars are actually meteors falling down on the surface of earth. How come some of them appear shooting up and not down?
Shooting stars are indeed meteors falling down, but consider this: meteors which are part of a meteor shower actually appear to come from a point in the sky called the radiant point: google image
Since you're looking upwards, you may be looking straight at the radiant point, and therefore the meteors are 'radiating' away from that point in all directions; not only 'downwards' towards the horizon, but 'upwards' from your point of view.
You can see that, even for a meteor which is not part of a shower, it's just as likely for a meteor to be going 'upwards' across the sky, as it is to be going 'downwards'.