So now three people know, not including the gender therapist, my mother, a close friend, and the doctor.
She asked about my having been admitted to the psychiatric clinic, as I told them it was fine to request records and such from the GP, and I just told her why I was there and all that.
Barring some awkward questions, she was mostly worried I might change to a different GP as she didn't have much experience with trans issues, I pointed her to the new team that just formed in the area and assured her I was only going to them for things that are trans specific basically. So there's no chance of needing to find a different doctor for all my generic concerns, yay! She wasn't aware of the new program, so basically if someone else under her care comes out to her now she'll know where to send them.