As already explained, a psychiatrist is generally an MD who can prescribe you medications - usually they stick to psychiatric medications like SSRIs, ADHD meds, yadda yadda. I wouldn’t be surprised if some psychiatrists also do gender health.

If your GP is a good one, they will take suicidal ideation and/or intrusive thoughts seriously and set up a consult for you with a specialist- or at least give you a number. Having intrusive suicidal thoughts is a serious thing to go through and from the things you’ve written, its obviously distressing to you. It can be hard to screen someone for suicidal thoughts, some people are more passive and others more active. Some people have the equivalent of something in their heads screaming at them to do it (not a hallucination necessarily, I know exactly what you mean when you said it) but they dont actually want to die. Im a nurse and do lots of intake, I always ask people straight up if theyve had thoughts or a plan to actually kill or hurt themsleves or if they’ve tried to before. I also ask if they’ve ever had thoughts of wanting to go to sleep and just not wake up (thats more passive suicidal ideation). I ask them, if they’re positive, for either that if I gave them a button that simply let them cease to exist and I left the room, they had time to say goodbyes or whatever, would they push it? That can tell the difference between active and passive.

I dont know what kind of therapy would be most valuable for you, thats up to your healthcare team (which includes you). I suspect some version of CBT would probably be the most beneficial. CBT when done properly has homework, its not just talk it out for a couple hours then wait a week. You have to work on identifying “automatic thoughts” and track them and write them down.

I took medication to help me deal with my darkest lowest point, and I ended up on it for about 18 months. I really valued it, it helped a lot with suicidal thoughts and my emotions. But after that long, a lot of stressors were gone (I graduated, got a job, had long broke up with my ex, etc), I had done a lot of therapy, and I felt ready to stop taking it and tapered off slowly for about 4 weeks. You may be advised or prescribed to take something like Effexor, like I was, if you do give it a fair shot to kick in before asking to switch. They take a while to come online, about 3 weeks is typical.