There have been various threads on pprune about gaining a Class One medical, having suffered a variety of mental health problems, some have suceeded. The position between one aviation authority may differ. Again aviation authorities may depend on a indepedant pychiatrist's report.
If you do get a class one medical and complete you training you have an ongoing problem is that might find it difficult to gain employment with an airline based on your medical records, although they might give another reason. Obviously after the Germanwing accident, airlines, aviation authorities and insurers are likely to be very cautious and nervous over mental health issues.
I'm sure this is not what you want to hear, but it would be very risky to spend say £100,000 on a pilot's training course, because of the uncertanty in respect of employment based on your medical records.
I have to say from my experience, I can think of several occassions when experienced pilots have developed anxieties in their thirties and forties, this included a RAF C130 captain, a BAC 111 copilot, and a RAF Tornado navigator. The difference is with you is that it sounds like you are at the begining of your career, and maybe you can build on your confidence and work on your anxety. I am a little sceptical about psychotherary, you are quite young and perhaps can resolve this now. We all find giving breifings, lectures and public speaking difficult at the begining of our careers, but it becomes quite easy. My suggestion you join a local theatre group, even if you start backstage, join a choir or in the UK there our evening courses on public speaking.
Finally, I think certain SSRI's are legal in the United States for airline pilot's, and I am not sure what the position is with the UK CAA, but whever you are, i doubt it would held if you have to declare taking them at the begining of your career., so you are wise not to take SSRIs.
Finally, there is another recent thread on PPRUNE - MEDICAL, regarding gaining a UK CAA class one with a history of depession, orginally he was turned down, but now has been accepted, you might want to PM him. best of luck.