They won’t delete it from your file
If something is proveably wrong then you can have it removed. So if this has not been discussed with you properly or has been written down incorrectly, then you can ask to have it removed as well as having a note put on or it hidden or both in the meantime. It isn't easy though.
You should have been offered a referral for a talking therapy to deal with catastrophising so if you haven't been, that's an error on the part of those GPs. And particularly given that you show awareness this trait shouldn't be held against you or given too much weight. If you have possible medication side effects it's very important that they are given attention and yellow carded whether or not they are 'definitely' side effects or not. Assuming you are a woman, be aware that women suffer from this kind of unconscious bias and dismissal of their concerns from healthcare professionals frequently (more than men but it happens to men too) - don't put up with it.
To a PP, don't believe for a moment that GPs and other medics don't write things like this down. It used to be 'TATT' with reluctance to act, in my case, as though that's reasonable especially in a young person (yep I had an actual medical reason for it which I had to push and push about). I also find actual errors across my notes quite regularly where someone has written the wrong term or something I blatantly didn't say which they have misunderstood or misremembered and probably written down after the fact. They are so rushed, it can't be easy, which is why we need to stay vigilant and speak up.
I also have a friend who had some things actually removed although he had to really fight for it. And other healthcare professionals kept coming across them not knowing (or more sinisterly, not believing, despite the corrections from other healthcare professionals) that they were wrong, in the meantime. It caused a lot of problems.
This is one reason why some people go to private GPs, counsellors etc. for some things.