You have my sympathies. I have urethral burning. I'm more comfortable before a wee than after it. I often feel like staying there and keep trying again and again.
I had this from age 27 though. Told it was urethral syndrome. I told the doctor I was worried about urine in the urethra leaking out, but I didn't have bladder urgency or anything, so I was only worried about a few drops of urine that felt like were stuck in the tube. Nothing ever leaked out, just very uncomfortable. After a while it would go away, until next time.
I asked for oestrogen cream then but I remember the doctor's words, she said at my age (then) I'd be 'dripping in oestrogen.' What a strange thing to say to someone with the problems described and the associated worry.
These days I do my best to ignore it, but while it's not painful or anything, it's very hard to ignore.