I’m going to just say that iron infusions can make you feel unwell, but if you’re at all concerned, just ask them to do the slowest infusion possible.
I had one where I felt as if I had flu for 2 days, but the next 3 were fine.
It takes 4-6 weeks for all the iron to be made into new red blood cells, but you start to feel better gradually before then. It’s not like they’re all suddenly made on day 28 iyswim.
Supplements can work almost as fast if you take the right kind, and a decent enough dosage.
My GP recommended 100mg a day, of ferrous polymaltose, but there are several sorts that won’t give you the usual iron issues.
Given that you’re having teeth problems too, I’d say you have a real problem with absorbing vitamins/deficiencies, and that you should pester for a blood test including vit B12, vit D, full iron panel (including ferritin), calcium, and as others have said, probably thyroid and others too.
The NHS bar is extremely low, and it’s simply not appropriate for everyone.
Crack on with taking an iron supplement, and some vitamin D3, if you have the blood tests, the ferritin will show your stored levels of iron, so won’t be unnaturally high from taking the supplement, your Hb might be though.
Good luck. If this works, it’s a pretty easy win. 