AnxiousGirl, we seem to have a lot in common with our therapy fears

It is very common. You just need to give it time. I am the exact same way--extremely reserved until I get to know someone. I started seeing my T at the beginning of my sophomore year of college. I'm in the 2nd semester of my junior year, and I am
just now starting to get comfortable with him. I actually had an effortless conversation with him yesterday. It was a rabbit trail conversation, but it was encouraging that I could
finally get to that level of comfort, if even for a few minutes. This is in stark contrast to my first several sessions, where I was horribly awkward and barely able to squeak out sentences because I was so tense and nervous.
That said, I still struggle with being able to spit out the serious stuff and always have. I'm personally a heck of a lot better writer than speaker, so I have written emails once or twice and have even typed up a letter to have him read. It's all up to what your T is willing to do. It sounds like your T will be able to handle this very well, though. I think it is more important to get to the things you need to deal with--whether it is verbally stating them or putting it in writing. The issues with communication can be approached when your comfort level is higher.