iPhone 4 hot on back and Battery drains fast

So I dropped my iPhone 4 last week, and during that time my screen was cracked but that was all, so I was still able to use it, and it seemed perfectly normal besides the cracks. Today I got my replacement screen, replaced it, everything went fine (I'm not sure if the screen is a 4s or just 4 if that helps). iPhone screen was originally black but now is white too. Anyway, after using it it became uncomfortably hot on the top of the back of the iPhone. My iPod touch 4th gen used to do this but when it was charging, but my iPhone wasn't, I was just looking at Instagram. I decided that I'll wait till later to see if it cools down, so I put a case on and kept using it. I realized later that I could literally watch then percentage go down on my battery, too fast.

--EDIT--

Thanks for the reply, but I think it is a board problem, the phone is hot on the back where the board is. Do I just buy a new phone or what?