Julian, we're close to the same age, and I'm just now making a real attempt at transitioning. I found that therapy was very helpful in many way. I don't feel the shame and guilt that my family heaped on me for being different, for wanting to be myself. Having great friends [mostly LGBTs] who are loving and supportive, and think I'm awesome just for being Amadeus is...well, wonderful! It's really boosted my self esteem and made me want to move forward with pride, dignity...and sh*t.
And there I go again, channelling Emily Howard from Little Britain. Pity it couldn't be Tom Baker instead...
Anyway, yes, go see a therapist, one that's LGBT friendly. Talk about your gender dysphoria, find out what your options are. If you just enter your city's name alone with 'LGBT friendly therapists counsellors' then you should get some good results. Once you talk to the therapist and find out the process, you can make long term plans and go from there.
As for your job, most medical employers are educated enough that they might bat an eye when you tell them you're transitioning. But that's about it. It'll probably be, "Oh, really? Okay. So, how's that working out? Do you have this paperwork? Are you having surgery?" Be prepared for questions not just from them, but from your family and friends. Be honest and polite. Be firm when necessary. Don't take any rubbish from anyone. Be true to yourself in all things. And best of luck to you