Hi Madison. It sounds like you damaged your digitizer when your phone decided to smack a wall. You have a problem called ghost touch. A simple screen replacement should fix the problem as long as you didn’t damage any other components on the inside of the phone. iFixit sells screens, but there are other places to get screens that are a little lower quality and lower priced. You would be looking at around $15 for a 6 screen from other places and a lot more from iFixit.
Did you do a hard reset after replacing the battery? That could be a problem if you didn't. If you bought your part from iFixit, there should be a little card that tells you how to calibrate the battery and that you should do a hard reset after replacing the battery. To do a hard reset hold down the sleep/wake button until you are able to power down, but don't. Then while holding the power button, press the home button until your screen goes off. It should then turn back on. Hope this helps Alec T.