Update #1 (11//09/2019)
I had a doctor's appointment today (earlier than expected because there was a cancellation).
My doctor thinks I may have endometriosis, which I had considered beforehand but wasn't sure about. It's where the uterus lining grows outside of the uterus - e.g. on the ovaries, on the bowels, etc. which can be really painful and cause some of the symptoms I was experiencing. However, it's very difficult to diagnose (can only be confirmed by an operation I believe) and the treatments at first are the same as 'normal' period pain anyway so it doesn't make much difference atm.
The first course of action is to try Mefenamic Acid.
I didn't think I would be able to have this as I already take Naproxen (which is almost identical) for something else and (a) it doesn't work for my period pain and (b) it makes me feel really nauseous and I was going to be asked to be taken off it. However she's also prescribed me Omeprazole, a gastro-resistant drug which should reduce the amount of acid in my stomach so it shouldn't make me nauseous - and I'll just have to not take the Naproxen for my other conditions whilst I'm on my period.
I'm not that hopeful for this tbh because it's basically the same as Naproxen, which I already know does nothing for me, but I'm going to give it a go for 2-3 cycles. If that doesn't work, we're going to look into hormone treatments, but because of certain medications I'm already on and also because I get migraine with aura, I'm limited as to which ones I can use...