What is my phone doing?

I hope somebody else has experienced this (not to wish this on others but just to get some help lol)...but at random times my touch screen literally spazzes out. For instance, if I go to messages and try to click on a person's message, the screen will just scroll all the way to the bottom of my inbox. Then if I try to hit back to get back home, it brings me to weird screens such as facebook or something else. Even if I do get to my messages and start typing, it types the most random letters that I am not even close to touching.

The weird thing is the phone will be perfectly fine, then do this for a little while, then be fine again for a week. Anyone else experience this? I have no idea what can cause it.

 

I don't mind doing a factory reset to see if that is in fact the problem.

Setting>Privacy>Factory Reset...correct?

One question though, would I then have to purchase apps that I previously bought or will I be able to just install them again since they are connected to my account?