Does it look like the home button is physically pushed down into the screen assembly? It sounds like the bracket for home button might have broken loose from the screen assembly. It might also have something sticky on the home button to cause it to stick. You are going to have to take the screen off and check what is the problem. You can change the home button but you will lose touch Id. The factory home button is matched to the motherboard so an aftermarket home button will work but touch Id won't. I would try to fix the original home button first.