I think you handled it okay. My phone calls with T usually last around 10 minutes, so 7 minutes would still be enough to at least say something like 'hey, I'm really not doing well, but I'll have to leave in a couple of minutes, can we please talk later, I feel like I'm going to self harm' or something like that, and I assume your T might have understood and made time for you later.

Him calling 5 minutes late is on him. Of course it's normal to sometimes be late, but if you said you have to work from 2 on, then he should have known that that would be really stupid.

I'd be annoyed as well. He first offered to take your call if you ever feel like self harming, then you reached out at a reasonable time and he offered a time slot which he then was late to although he knew you did not have much time anyways. This is totally on him.