I sympathise with you OP.
However, you need to be aware that gynae doesn't automatically mean hysterectomy.
I've been wanting one since I was 25, for similar reasons to you. At 25 I was told too young. At 30, too young and not married and symptoms may calm. At 35 and with it getting worse, a flat no.
I finally got a good GP to refer to gynaecology. First time it was even considered. She wrote a brilliant referral for me and marked it urgent.
That was in April 2021. I was told to call them if I heard nothing by June due to it being marked urgent.
When I called was told they had triaged as non-urgent. Asked them how do they triage without seeing me. Was told "they just do".
I got sent an appointment for December 2021, which was then cancelled two days before until the end of January 2022.
Got to the appointment, the first consult ignored my appointment time and saw a lady with her husband first. I was waiting for 2 hours until I said, you know clinic finishes in an hour am I going to be seen at all?
They then send me through to a female and I thought, that's great because she will show empathy.
She wouldn't listen to my symptoms or look at my diary which showed how bad things get. I explained that I had tried other methods of contraception and things but these had made me ill.
All she was bothered about was "they won't fund it" and "you'll need to go private". She said I "had" to have a IUD fitted first, admitting that this would "probably go wrong" because of my insides being wonky (birth injury), but "at least they will let you have your own way then".
I left in tears.
I contacted PALs who got the head consultant to speak to me who wanted a scan done to see if an IUD would be bad for me.
They forgot to book this. Finally got one sorted to be forgotten in the waiting room. I then had the scan but the tech noted issues which meant she couldn't do an internal scan.
Felt like finally they would have to act. When the lead one called me she sounded smug. Said nothing found. I told her I knew that was rubbish as the scan tech saw and noted huge issues. She then said that no matter what, it's not a procedure they will fund and at 40 I'm near menopause so who cares basically. I have no idea what age women in my family have menopause as I'm N/C. So potentially could be like this or worse for years.
If you can go private do so, the NHS have little consideration for female health at all. We are pound signs to be cut.