I agree with everything that has already been said.
It sounds like you are reading way to much into this relationship.
Your T is a professional who is there to help you with your problems, that is all. It is their job to be nice and friendly and to develop your trust so they can help you BUT you are a client in their work life, they have hundreds of others and although they have a genuine wish to alleviate your suffering, their relationship must be professional, independent and objective otherwise they will not be able to help you.

Maybe you should set up some boundaries about replying to emails; if you are constantly emailing her, what do you expect her to do about your emails? and what can she do in between appointments? if you are in danger she can get someone to take you to hospital but other than that what can she really do?
It is good if you can use emails to communicate things that are important to you that you might not be able to say, many people find it easier to write something down to give to their T rather than say it, so T knows about things but this is just a form of communication and she is right to save it for the next session.

I am worried about you Dustin, you sound obsessed with T, thinking constantly about the next time you get to see T and this is dangerous, I hope you don't progress to become a stalker.
You and your life are so much more than just seeing T - I can see you getting extremely hurt and just want you to be careful and keep check of your feelings.

I hope things start getting better soon, but you are clearly in a lot of pain