Peri-menopause is not easy to treat with HRT so its all about trial and error. I personally had to use a private doctor and am using the compounded hormones too but that is because I couldn't get the more specific doses on the NHS but if you're lacking oestrogen then the NHS should be the place to start and much cheaper. Maybe you could ask your GP reception for an appointment with a GP who is more knowledgable with HRT and if no-one is, ask for a referral to a menopause clinic.
Re. the nausea, I also had it really badly and lost so much weight I had to just sip milk throughout the day to avoid dehydration as could not eat and had to take a few months off work unpaid as most days I couldn't leave my bed. I was also told it was a virus and endless other gastro things like ulcers, but had to wait 6 months for the gastro referral to come though to prove it wasn't, and no-one mentioned it could be hormones. I'd accepted it was a mystery illness, as the docs started to turn me down for emergency appointments "as I'd already been that week" and I remember making myself feel better with the thought that at worst I could go to Dignitas?!! Anyway, once I realised I was always in A&E during my period I figured out the hormone connection and a GP put me on the BCP pill which after 7 days of making the nausea worse (but knowing it was hitting a spot which gave me confidence), it all just STOPPED. I have never felt such relief in all my life to get 'off of that boat'.
I've since found the nausea was so bad as my endocrinologist believes they are migraines being triggered by the hormone imbalance and I do not know if going straight on the natural HRT then would have worked, as things were so severe, and I have had moments of it (around ovulation) but for me the pill being so much stronger would be what I would reach for if I wanted to ensure zero nausea. Hence, it might be useful for you (and the high synthetic hormones calm your own cycle down more than a Mirena could as that is only progesterone) just to get over the hell you are in now if you can't get the right HRT you need if have to wait to see someone else. Anti-histimine type anti-emetics, like Cyclizine, may also be of instant relief but they do make you drowsy, the other anti-emetics made me worse but all are worth a try when you're that ill.
Good luck!