First visit to a NHS GUM clinic, an alternative view to the OP's:-
I had my first experience of visiting one (Bristol) 18 months ago ... a Positive rather than Negative experience.
First you can "walk in" or make an appointment.
I chose to "walk in" and arrived at 10:30 am.
The first surprise was how big, bright and airy the reception and waiting area was. How busy it was and how normal everything seemed. People, both male & female, just sitting there doing what people do when they're waiting, eg reading books, playing with their phones etc. Nobody looked up, no one stared, no one was bothered about who else was there.
The second surprise was being given a card and asked to return at 3:30pm, yes, 5 hours time! However, before I left I was asked to complete a form. Side 1 - Personal details (I guess if you're really worried you might get away with faking these, I didn't, I just gave my real info), Side 2 - Why you were there. You're given various options which probably cover most of the reasons why you might want to visit such a place.
I was told that, although I'd been given a time slot, it was possible that there might be up to an hour delay.
I duly returned at 3:15 pm hoping that they might be running early.
This time I was directed to a male waiting area and the third surprise was there was not one, or two, or even three doctors/nurses but six! just for the males (alright it's a big city).
Finally, at 3:50 pm, I was called in by a young, female doctor.
I confirmed who I was and why I was there. There was disclosure of relevant facts, yes, a few details relating to my hobby (I indulge in FBSM not FS). I'm sure she's heard it all before.
Then it was on with her rubber gloves, a bit of groping, two swabs taken (yes, one made me jump and was painful) and an "armful" of blood taken (I'm of the Tony Hancock era) then off to the loo with two bottles and a pipette. The clever bit being a hatch from the loo to their analysis area so you don't have to carry the bottles back.
A short wait in reception before being called back in to be told the initial two tests were clear, ie no infection present.
Then a two week wait for the results of the other tests but with the reassurance that it was very unlikely they were going to identify anything nasty.
Phew! Panic over.
HOWEVER, the main purpose of writing this is:-
IF IN DOUBT, GET IT CHECKED OUT.
The whole process is as normal as normal can be, don't be put off by the OP's comments.
Ages? There was at least one person there over 60.