You're overcharging the battery by using it while plugged in at 100% for long periods of time. This causes the battery to swell and press against the screen.
On your new battery, keep the charge between 40 to 80% while plugged in (yes, unplugging it at 80%) and run a charge cycle once a month from 20% to 100%. The battery will last much longer and won't swell.
Use the app below to help remind you.
Low Battery - Phone battery power glance & notifications by Ben Guild
https://appsto.re/us/3ed2N.i
What about leaving the iPhone on charge at night? Does that damage the battery? I often do that, then when I wake up in the morning it's at 100% and ready for the day.