Touch Disease is a very common failure on the iPhone 6 Plus.
At first, the phone will typically develop intermittent touch control failure. For some phones, a gray/white bar starts appearing at the top of the screen. Twisting and applying pressure in certain spots sometimes allows touch control to work for a short period of time, but eventually, the touch interface ceases to function entirely. This is colloquially known as Touch Disease.
If you are confident that your replacement screen is fully functional and there is no damage to the Digitizer FPC connectors on the logic board, then your phone probably suffers from Touch Disease. This is not a DIY repair.
The current best practice for permanently repairing Touch Disease on the iPhone 6 Plus is to solidify the M1 pad underneath the Meson Touch IC. That pad tends to lift, partially or totally when removing Meson.
Look for a repair shop that can do micro-soldering repairs to properly diagnose your problem.