"My T doesn't want to support me even when this happens"
Granted, this might be his policy but does he give you coping skills or strategies for moments when you feel overwhelmed? If not, this would be something to explore with him. I.e. give you something to 'keep you together' in-between sessions, maybe as a temporary fix until you next meet with him. For example a 'support' voicemail that you could replay at such moments etc.

More generally, could you tell him what you need e.g. some gentle encouragement, more attentiveness, or whatever you need really, rather than a simple "ok talk" to get you going? Maybe being (more) explicit as to what you need might help him help you better.

If he is not forthcoming and you need more support in-between sessions, could you look around for some other Ts? From what I gather here your T's style seems rather 'clinical'. You might feel more supported and heard with a T whose style is more caring...