Is it possible to only have the lcd in your iPhone broken, and not the screen. I have am I-phone 5C?

Yesterday I dropped my iPhone 5C, it didn't crack, but the far right side doesn't react if I press a button on that side. It also glitches, if IIm on a page and scroll down it will go scroll right back up to the top. Lastly, the lock screen doesn't react at all for about 15 seconds.

Obviously you damaged it.