Oh wow... I agree so strongly with Susannahsays re: your T being unethical. She knows your struggling with self harm, and expects you to go months between appointments?
I'm kind of peeved at her on your behalf.
You deserve better!!! And, I agree... emergencies happen... but just like she expects flexibility when she has an emergency and has to cancel with short notice, she should also *give* flexibility to reschedule you, especially given what you're dealing with, so that you don't end up having to wait another month b/c of her schedule. To me, it would be appropriate for her to work an extra hour, for example, to fit you in on a day sooner... given that your appointment disappeared through no fault of your own.
Ugh, I'm so so sorry. Hang in there. (And if you're up for it, definitely consider looking around at the other therapists - it sounds like there aren't a lot of good options by you, but just in case you manage to find one hiding somewhere nearby!)
*hugs*