Screen not responding/has a mind of it's own when typing after repair?

Basically, I dropped my phone, screen-first, onto a hard floor. It cracked really badly. I thought to myself, "I successfully repaired an iPhone 4S screen many a time, and as that involved taking the phone to pieces, how hard can a 5S be when you remove the screen from the front, right?"

Wrong.

I watched the iCracked YouTube tutorial (I didn't buy my screen from them, I got it from Htechy). I realised you had to replace the button (which the hole didn't line up with on the screen, despite the screen being a more expensive one) and the camera and speaker and all that jazz. I did it all, put it back together and it seemed to work fine. Home button was a bit sketchy with the placement of, but it worked completely fine. The ear-speaker and front-facing camera worked too. I thought "Brilliant!". But after a few minutes, the screen would not respond to my touch or would type by itself (i.e. Spam a key. Usually on the left side such as E and D), but only for a second. After a few hours, the same problem kept happening worse and worse, but I would just lock my screen and unlock it and it would work pretty fine. But now, 2 days later, I can barely use it because:

It types by itself
It scrolls by itself or rejects my swipes (i.e. To close apps after a double tapm of the home button)
It won't pick up my touch
I don't know what's wrong with it and I don't know how to fix it. I can try fixing it if I know the issue. I doubt any phone shop would touch it now I've done it, either.

I have the same problem with my 5c. I just used it and it would normally fix itself after it got hot. But take it to the shop if you want it perfectly newish