We have a white goat that as of lately, seems like she could be sick. She has been eating just fine, and seems as though drinking and is still just as friendly, however, I have noticed her behind is really dirty, her tail, back legs, the whole back side like she is dragging her bottom like a dog sometimes does. Is this a sign of being sick, is there other symptoms I should be looking for. I have seen her poop, it almost seems like she could be constipated, if that is true, what do you do? We have several fruit trees and have been throwing the apple and pears over the fence for them to eat, is fruit bad for them?

When was the last time you wormed your goats? It sounds like she might have worms.

I hate to admit this, we have never wormed her, she was given to us, we don't even know how old she is, I think kind of old. We have one sheep too, could this affect her also?

Unlikely that the sheep would affect her. Goats and sheep get along just fine.
If she's never been wormed you DEFINITELY should worm her, as well as any other goats you have and the sheep. Your animals need to be wormed about twice a year. It only costs a few bucks and it's pretty easy, you just stick a little dispenser in their mouth and squeeze it.
We have around 100 goats between my parents farm and my grandparents farm, so we keep on a regular worming cycle of doing a few a day most of the time.