Go to your GP with a list of symptoms (written down so you don't forget or get emotional), a list of last periods/times between them.
Also take a print out of the NICE guidelines on menopause so they don't try to fob you off with anti-depressants or similar. Highlight the bits that apply to you, and make sure they know that you've read them.
If you're over 45 you don't need a blood test or anything else to 'prove' you're menopausal, just your symptoms. If you're under 45 they might offer a FHS test, but it's only good for that moment - everything fluctuates, so a bit meaningless.
Ask specifically for the medications you want. Oestrogel and tostran. The coil was for contraception, but just progesterone, so you might be able to take pills instead. I didnt want to use patches, but some of my mates have preferred them to the gel. You'll probably have to do the O and P combo before they'll let you try T. The O and P might fix your issues.
I saw my own female GP who told me I wasn't menopausal, she told me I didn't need anything because was too young. I waited 3 months then went back to see a different GP at the same practice. She told me the same thing, i made her look up the age for FSH test - i was under 45, she relunctantly agreed. Had test, got result. Off the scale menopausal - not peri, but fully done. She told me that HRT side effects for me would be 'death' from blood clots. I cried.
Booked another appt 2 months later with my NICE guidelines (I did a lot of reading, Liz Earle was the place to go), I waited for an hour then was told sorry the Dr had gone on an emergency. I lost my shit. Cycled straight round to a different practice and joined.
A month later I saw a male 50+ year old GP. Was not hopeful. He was fricking ace, I loved him! He gave me a referral to the menopause clinic to check that I could take it with my blood condition. I could choose where I went, so went to 'the' one near me - had to wait 4 months for that appt. When I walked in, before I even sat down she said 'ok, you can have HRT, so breathe out and we'll have a proper chat about what you want.'
Sorted. Already had sorted myself out with a mirena coil by this point, but got the oestrogel. Had regular blood tests to check levels until I settled at a sensible bone protecting level. Had testosterone after 6 months when no increase in libido.
Hot flushes and brain fog went within 6 weeks. Libido still comes and goes a bit, lockdown hasnt helped with that!
Have been told to stay on it for 10 years minimum. Breast cancer and blood clots are in my family, so I'm paying for private mammograms once a year.
If I was starting now I'd go in fully armed and not ask for advice. I'd just say what I wanted.