The psychiatrist does not prescribe the T - they write you a referral to see an endocrinologist, who is the medical professional that prescribes you the T.
When you get you referral depends on the psychiatrist and what standards they follow. Don't expect to get a referral the same session you "come out" to them. Chances are they are going to want to discuss it with you - the pros, cons, why you think you feel this way, what you think the outcome of transitioning will be, social, personal, your hopes and goals, etc etc. They could be satisfied within a couple of sessions, or may require more than that.
I don't believe the sessions have to be "regular" (IE weekly).
From what i've been told not all therapists or psychiatrists can write these referrals, so you HAVE to check that yours can - which means asking them. If your therapist or psychiatrist does not have much trans experience, even if they can write the letter, then you might want to find one that does anyway just so you know you're getting good and accurate advice and information.
And that's just the first step to getting T. Once you've got your referral you have to find an endocrinologist. It may take one or more visits with them to get your script... or at least get your first dose. Some may require you to come back a couple of times for your dose, before letting you do it yourself. Then you've got regular blood work to think about. But we're getting ahead of ourselves!
If you want to take the next step, you have to be open about it with your psychiatrist. You're worried that nothing might happen even if you tell them? Well, nothing DEFINITELY will happen if you stay silent. Telling them is the first step. They will guide you from there, it is their JOB to do so even if it means referring you to a specialist for further aid.
Good luck!
