about my display screen

While either heat or pressure can damage a screen, it's unusual for an overheating phone to get hot enough to mess up the display, so my guess would be pressure damage from rubbing the screen hard. However, a picture is worth a thousand words, so adding a photo of what you're seeing on the screen would help us better figure out what's going on with it.

Adding images to an existing question - iFixit Repair Guide

That being said, it's almost certain that you're going to have to replace the screen to fix the issue, as neither problem is going to get better by itself. On your phone the recommended way to replace the screen is to buy a screen that's already attached to the frame, then you have to basically gut the phone and transfer all of the internal components to the new screen+frame assembly. It is a bit of a daunting task, especially if you haven't worked on a lot of phones. Here's video showing you all the steps you have to do to make that repair.

Nothing Phone (2a) Plus Screen Replacement - Step-by-Step Teardown & Repair Guide - YouTube

The other way to fix your display is to replace the screen by itself without the frame. That procedure is completely different from the first method and needs a separate video like this one.

FIRST NOTHING WE GOT! Nothing Phone 2a Screen Replacement - Sydney CBD Repair Centre - YouTube

With this method you only remove enough parts inside to access the display connector, then you have to separate the old screen from the frame, clean off all the old adhesive, then glue a replacement screen on. The screen by itself is only going to be slightly cheaper than the screen+frame assembly, but you may make up that difference by having to buy glue (unless your replacement part comes with it).

Either way you choose, that will fix your display problem. If for some reason the screen was damaged by internal heat, you may need to try and fix the overheating issue or you'll be taking a chance of ruining the new screen just like the old one. I'd consider a battery replacement as the first step, as a bad battery can be a common cause of overheating.

Good luck, and be sure to come back and let us know how it all turns out; your experience could help the next person who has the same problem.