iPhone 11 screen laggy after screen replacement

The iPhone 11 screen is very laggy and sometimes registers pressing as holding, it works slightly better with low brightness, but it rarely works without any problem after turning it off and on again. I didn’t have a problem with a „reproduced” screen, but when it broke, I’ve cheaped out and bought a worse screen because it had some good reviews. Can the screen quality be the issue in this case? Also, heavy games like Wreckfest work perfectly fine without any frame rate drops whatsoever if it has to do anything with the „lag”.