Firstly, you need to get a serious advocate on your side and if you're in the States I'll go so far as to contact the local chapter of the ACLU and share with them all the gory details (they love this sort of thing... especially when the people in the seat of authority seem to be talking out of either side of their buttocks).
I have dealt with very dangerous anxiety-depression issues for much of my life which is compounded by a small cornucopia of physical health issues. I'm more than familiar with the bias that can be experienced, the most recent one I'm dealing with are the handful of folks who don't understand the idea of "Limited Mobility" i.e. why I can stand and walk short distances but also use a wheelchair... people don't understand that MS, at least in the stage I'm in, can flare up and then go years without creating more problems (which is why it is called "Relapsing Remitting Multiple Sclerosis").
My second issue is that if the school isn't going to let you go, why did they accept your money in the first place? Why didn't they address this prior to departure time?
That's non-professional and highly unethical in that their argument of concern centers on your depression issues and yet, their actions (almost premeditative it seems) are of the sort that would deliberately create an anxious & depressed state in a person... between you and me, I'd say you need to talk to a good lawyer and hang them with a nice big law suit due to their cruelty in this manner. I'd also shoot for two separate suits; one with the school board and then another towards the individual(s) that suddenly put this road block in your way AFTER allowing you to pay the money and get your hopes up. I'd sue for that SOB's job in that he/she is unfit when it comes to monitoring young people and seeing to their NEEDS in a positive, supportive PROFESSIONAL manner.
The real issue here is NONE OF THESE TEACHERS are clinically trained when it comes to calling the shots and I have high doubts that they would have pulled in a legitimate expert to look at your situation prior to making this decision.

Sorry, but this story irritates the hell out of me. Seen far too much of this kind of KRAP over the years.