I don't know if anyone else does this, but since I was really little there was always this certain fabric that I would run against my lip. It's just a habit I've been doing since I could first remember it. If someone has the same problem, is there a name for it or does anyone else do this? Am I the only one. It's like a stress reliever and it also helps me fall asleep. Anyone else do this?

I don't think there's a name for it, but I wouldn't be surprised if plenty of other people don't have something similar. I had a 'habit' for much of my young life (don't know when I stopped) of lightly running my lips over the little hairs on the back of my hand. It isn't really an addiction unless you are compelled to do it constantly, especially in situations that are embarrassing.

It's probably simply a subconscious type attachment to fond memories from when you were young

There is a skill that can help lowering your emotional response that I learned. It uses the 5 senses of which touch is. There is nothing wrong with doing it. If it helps lessen your stress levels and high emotions great to you for finding a coping mechanism.