Do I have any options?

Doubt it. You could have said no, why didn't you? It's also kinda stretching the realms of reality that a doctor would have a 12 year old child at their work let alone ask them to stay during peoples intimate appointments or not take the patients wishes into account.
"Why is there a random 12 year old in my doctors appointment?"
'He's my son, is that ok'
"No, not in any circumstances whatsoever"

The doctor let her 12 year old son see me completely naked. Why can't I sue her?

I would think your Mum consenting would put the kibosh on that one.
Why she would think that was appropriate I cannot fathom.

Why does my mother consenting prevent me suing? The doctor asked if her 12 year old son (a minor) could see a 14 year old girl naked (who was also a minor). Why was the doctor allowed to do this just because my mother consented? There was no reason for the boy to see me naked.

The doctor let her 12 year old son see me completely naked. Why can't I sue her?

Honestly, because most people will think it's made up, it sounds farcical that a doctor would do such a thing and just happen to meet your mum who would allow such a thing. If they were bringing their kid to appointments they would be buried in complaints the same day imo

I agree with your last point.
However I am saying that your Mum being completely fine with it, and consenting to it on your behalf, may well have hampered any potential legal action.
Is this all hypothetical, have you got funds to hire legal representation?

Would a solicitor be able to help if I contacted one?

Why would my mother consenting to it hamper legal action? My mother could give me permission to steal a car but that would not be legal. The doctor made the request.

She has duty of care regarding medical treatment like all parents of minors. The same reason that she chooses where you live and go to school.
The doctor made a request unrelated to treatment, a request can be refused, but she apparently saw no issues and made the choice for you and you went along with it without any noted protest.
So regardless of what request was made, she's the one that said it was ok on your behalf and has to legally accept some responsibility as your parent making care choices for you.
None of this still explains why you didn't say 'No, are you f*****g mental?', even if you had walked to reception and said 'I'm being pressured to undress in front of a random 12 year old' they'd have prob called 999.

But my mother choosing where I live and go to school is a reasonable choice. How is letting a 12 year old boy see me completely naked also considered a choice my mother can make? That is completely different and not reasonable.

I've no idea. I don't know your mother and you'd need to ask her, that's why I'm asking who you would sue, as she's the one that said it was ok on your behalf and you apparently had no issue with it at the time.

I would sue the doctor for letting her son be in the room and see me naked.

Four years ago, when I was 14, I had a skin infection on my thigh and chest area and my mother took me to the doctor. The doctor asked my mother if her 12-year-old son could stay in the room while I was being examined and my mother consented and they let the doctor's son be present while I was completely naked. I'm female. Can I sue the doctor?