This advice is offered from my own life experiences:
It sounds like your suffering is 100% from gender dysphoria, not depression. The cure for that is transitioning. Please do not check into a mental health facility because they will take away your access to hygiene products including shaving your face. Suicide is not the cure for gender dysphoria, and neither is psychiatric medicine. Don't let anyone tell you that depression is a stronger force than the true source of your sadness (dysphoria).
I think you should move to whichever country is the most trans-friendly of your options. When you get there, find a way to get health care access as immediately as possible and tell them you are suffering from extreme gender dysphoria that is making you feel like self harming (for example cutting your genitals) rather than suicidal. That should shortcut around the bs of doctors misdiagnosing or trying to talk you out of transitioning. If they give you a long wait period, make sure you periodically tell them how the extra time is adding to your suffering.
Make sure you tell people your real name (Jessica) and that you need to be refered to as female. This includes proper pronouns. If you ever see the wrong gender or name written on any health forms, ask to have it changed even though they probably won't let you. Always ask. Make sure you at least try to use the correct gender bathroom.
If you're trying to get as immediate of relief as possible, please make a list of what you want. This means asking straightforwardly for HRT (Estradiol, Spironolactone, and possibly Finasteride), facial hair removal (insist on electrolysis), be prepared to say that electrolysis is not cosmetic but rather medically necessary, and also be prepared to answer the inevitable question "Do you want sex reassignment surgery?" The more capable you are of answering these questions with very specific answers, the more likely you will be taken seriously and actually get the treatments you need.
I hope this helps. Best of luck. If you need any other ideas, don't hesitate to private message me.