Can I replace my glass screen and fix my problem?

So I recently cracked my phone (badly) and I was able to see and touch my whole screen but after a while my phone acts crazy as in it will randomly touch the other half of the screen. The phone is only cracked from one half so maybe that's the reason why it acts if I'm touching the screen? And some of the glass screen is missing. I was wondering since I know the digitizer works on one half of the screen can I just buy the glass screen itself and fix my problem or will I have to buy a new digitizer as well?