I've wished I wasn't trans many a time. It sucks. But it mostly sucks because our society refuses to acknowledge that we exist. Somehow, less "advanced" peoples worldwide figured out that trans people exist (although sometimes they don't draw a line between trans and gay, which are different things with similar etiology!). But the West since the dawn of the modern era (let's say circa 1500) has steadfastly refused to acknowledge we exist. (Even when they were reviving ancient Western texts that refer to other genders.)
The West "rediscovered" us in the latter half of the 19th century, when, we, with bodies not tailor made for the needs of the industrial world, were labeled, pathologized, called pathetic and crazy.
Trans is not a psychiatric condition. It's neurological. It's other people that give us psychiatric conditions like depression and anxiety, dealing with them.
I've been on T for 7 weeks. I find myself remarkably less foggy and fuzzy. I thought it was due to depression. Or allergies. I thought I would be that way for the rest of my life. Dena on this forum likes to say our brains run better on the correct hormones. I didn't believe that. Well, experiencing it is believing.
As for your question, you can go to the doctor and say, "Hey, I hurt my arm" but they're still going to do some diagnostic questions and tests (like moving and touching your arm and shoulder) before they come up with a diagnosis and write a prescription. Doctors like endos and surgeons generally, not always, would like another medical professional to sign off on your diagnosis before they go forward. That's not a ridiculous ask, but the problem comes in because some therapists are gatekeeping, powertripping <not allowed>. So the whole trick becomes finding the "cool" therapist who will write you a letter with minimal expense, wait, and ,<not allowed> (like telling you demeaning things).
The alternative would be for the doctor to attempt to diagnose you. I think most aren't comfortable with that because they aren't as familiar with the dizzying and bizarre bestiary of conditions you can come across psychiatrically.