I can understand your worries about this.
Last year I actually got to go to South Africa for 10weeks, doing voluntary work. I was living with a family (there were other English volunteers, but they were each with different families in the village)
I explained my situation beforehand to the organizers here in England. I was fortunate enough that where I was going wasnt as traditional and conservative as other parts of Africa/South Africa. I.e some of the girls wore trousers etc. I had been on T for awhile, but I assume you are not on T?
Are there people you can talk to before you leave? Explain the situation and see what their advice is? They will know best, and can judge how people where you will be staying, might react and take things. If I were you and was told to wear a skirt, Id scrap the whole thing. I have also dealt with severe depression and some anixety issues, but I found I was fine (although the issues ahev lessened dramatically over the past year or two.)
Not to sound harsh or anything, but you will need to take into consideration, how well you pass. It could lead to bad and uncomfrotable situations if you go, wear trousers etc and you dont really pass and people notice. Either way, I think you should speak to the head about this. See what they say.
Good luck anyway.