Hi Jasmin
You may have already been on the national Migraine Centre site and seen this information on menstrual migraine and contraception:
https://www.nationalmigrainecentre.org.uk/migraine-and-headaches/migraine-and-headache-factsheets/menstrual-migraine/
I think like Springer said you need to push your GP for a neuro-otologist or neurologist referral and in the mean time if you can possibly afford it see someone privately (and if you like them get on their NHS list If you are in the UK). Have you tried taking an abortive like triptans and/or an Nsaid like naproxen when you get menstrual VN symptoms? Your GP can prescribe these. You could also start on a preventative like pizotifen, amitriptyline or propanalol - build the dose up slowly whilst waiting to see a specialist.
I can see that a gym would be full of triggers - clanging, lights, loud music(often) lots of movement - you could try to do some more gentle classes for a while like pilates.
There is no one definitive migraine diet - some are more prescriptive than others. They tend to be informed by the trigger foods that patients have reported to specialists. Do you think any foods are a trigger for you?
There are threads about supplements on the site and this poll: