Ts are not supposed to hand clients tissues because it could be interpreted (by some but not necessarily all, and your T doesn't know exactly how you would interpret it especially when you are upset) as telling the client to stop crying or to pull it together. Because some clients could interpret it that way, Ts are supposed to be careful and not do that.

My T asks what is wrong (I've only cried twice uncontrollably in t and it started at the beginning of session so she didn't know what was going on.) She has told me that she is there with me.

The few times I have cried while we have talked, we just went on talking. It was kind of like she was ignoring it, but at the same time it made me not feel self conscious.