I had a similar problem with my 1.25 year old 6+. White line at the top that would sometimes widen into a thicker line, freezes, random acts of apps.
Reboots, reopenings, and even pressing on the phone often helped for a bit.
As I've learned from the posts linked below, and my visit to the Genius Bar, it is a known issue with the 6+. Fortunately I live in NYC and there are many Apple Stores. I went to one with a big Genius Bar the other day. Maybe 100 people between customers and staff.
I was anxious to make sure that the problem was occurring while I was there. So I opened tons of apps and made the problem appear. The helpful staffer explained that this a common problem with the 6+. He offered me a brand new phone for $329 as I was off warranty. He explained that "it can't be fixed" which I didn't quite believe one poster linked below opened his phone and fixed it.
I have the sense that Apple is reluctant to acknowledge this problem publically for various obvious reasons. And I guess it is cheaper for them to simply swap for new phones for those with coverage, or sell new ones at wholesale price, than paying staff to open the phone and do the fix
https://discussions.apple.com/thread/7028290?start=270&tstart=0
Bennett