Chosen Solution
I have fixed many screens, faced many issues, and have never had to post. Unfortunately, an iPhone 6s screen will not fit back into the phone properly. The frame may have slight bending but it shouldn’t be causing this. The issue is on the top right corner of the phone I think. When I push the screen in, the right side goes perfectly, and the left side does not. It starts about half an inch from the top and basically goes all the way down, resting above the phone. I was thinking maybe it was the battery, but I don’t really think so.. it seems to be an issue at the top left corner. Let me know what you think PLEASE!! Update (01/06/2017)
take the battery out and see if it will fit then to ensure your battery doesnt have any swelling to be pushing screen up. I had a similar issue with 6s plus and my problem was solved when back camera shield was seated properly. Hope it helps.
you can see that on the 2 picture that on the middel left side the clasp that hold the screen down is bent, my advice is buy a new backhousing whit preinstalled flexcables and buttons for easy repair it only cost $ 25,-