Definitely get the catheter if you haven't already, OP. I'm a bit

that you left without it, tbh.
A&E is for what it says - accidents and emergencies. Unless it has a sudden onset, urinary retention is not an emergency, and they were willing to deal with this by giving you a catheter.
I know (all too well) how awful it is to have to live with chronic pain, but it's not an emergency and they gave you pain relief. You really need a gynae referral, and if you can't wait for the appointment, scans etc, you can see someone privately.
The initial consultation is not that expensive, and if you see a consultant who also works in the NHS and is prepared to treat you on the NHS, it can save the waiting time for an NHS appointment.
Your GP will prescribe you pain relief to help in the meantime. Ooh GP can send an electronic prescription to your nearest 24-hour pharmacy if you need it now.
Waiting times are dreadful, partly because for months they weren't doing any non-urgent stuff because of Covid, so the waiting list got longer and longer, but also because of ten years of austerity and under-funding. We're back to where we were in the early-90s, when I waited 2 years to see an ENT consultant and another 2 before I had surgery.
I just hope people remember this come election time.