You can do a simple test on your phone to see if your screen is in need of replacement.
Hold Power + Volume down + Home Button. That should bring you into Download Mode, if it displays then your screen is fine. Otherwise, you will need to replace the screen [https://www.youtube.com/watch?v=4-Ca9C8QCS8|Instructions on the Screen Here (first step).]
Fairly simple if you have the tools, if not just bring it to a tech. After they replace the screen they can test other functions that may have been damaged from the drop.
Hope this helps.