Furryface i don't have experience with Norethisterone, i can't remember what medicine i had been given to stop the bleeding but i don't think it was that. However, being a progesterone pill, it'll do the job it's meant to do and will stop the bleeding so i think it is useful to take. Unless you take it for a long period of time, any possible side effects that might affect you, would go away once you stop taking it. So i would take it if it was me in your position.
It's good that blood test has been done for anaemia and tyroid. However they do not give clues as to why bleeding happens in the first place ie hormonal upheavals or polyps or fibroids...
For that, you need to insist on a scan. GP cannot view what's going on inside the uterus, ovaries. In that I agree with PollyPerky
In my case even with ultrasound scan, it wasn't possible to see one side (ovaries-etc). I had a little camera inserted, keyhole surgery style, to view inside and definitely establish the existence of the polyps. Once they could see the polyps and their exact places, they could remove them. That's only a 15-20 minutes procedure, nevertheless required more than the doctor's visual inspection.
Maybe your GP wanted to examine in terms of taking a smear swab which would be useful if you haven't got up to date smear result. But still it wouldn't help the whole picture. Booking an ultrasound scan, is the good practice which you need to get.