I am not much cop at asking for stuff that isn't offered, so can't help there. If you say that you know you had a cyst and you're worried that it might have developed further because you have this catalogue of problems, I don't see how any GP could not propose it. Do you have a good relationship with your GP?
I had to go to the hospital gynae clinic for my ultrasound scan, which was done by an ultrasound operator (who said nothing about what they could see, just did the technical stuff and made me comfortable), and then went straight on to see a consultant. After they had seen that my lump was solid, I also had some blood taken to test for ovarian cancer markers. Sorry if that sounds really scary, I just thought I should tell you everything that might happen as I felt shocked by this even though it was very unlikely that I had anything so serious.
On the other hand, I once had a scan to just check whether anything had changed, and I didn't see a consultant that time. The same person did the ultrasound and told me what they could see, and they sent a report to my GP who interpreted it with me.
So there are different possible models, and I guess what happens depends on various factors.
As for requesting a woman, do you mean at the GPs? Most practices are used to that. At the hospital the consultant was male. I have no experience over making specific requests at that level, though I guess gynae departments are used to answering questions like that. I just wanted to see someone who knew what was what, and he was really lovely, plus they are very sensitive to the way people are feeling, covering you with a blanket, having a female nurse present, etc.
Get on the road to sorting it out so you can feel better. Sending you good wishes.