Do stars follow us, because one day I was looking in the sky and it seemed that way?
If by "follow us" you mean that if you're driving down the street, you should see the stars remain in the same position in the sky even though you're moving, the answer is yes. The stars are much much much farther away than any distance you can move on the Earth, so you shouldn't be able to see them "move" on the sky just by moving on the Earth.
One thing to keep in mind, however, is that the stars do move slowly over the course of the night. The entire sky rotates about the point in the sky where you can find the North Star. You should be able to observe this by looking up at a constellation early in the evening, and then looking for it again a few hours later. You should be able to see that it's moved.
It's important to keep in mind, however, that the stars aren't physically moving around the North Star. It's the Earth's rotation on its axis that causes this effect.
This page was last updated June 28, 2015.