Bleah, I know what you mean about trying not to be a burden. I email my T between sessions (started doing it maybe 6 months into therapy when she offered). I find it really really helps me to get things out as I'm feeling them. It's too much pressure to hope that I'll still be feeling them and able to talk about them by the next session. I'm otherwise pretty contained in session, this is the one area where I'm more "needy."

One thing to think about is whether your T would actually consider this contact a burden. My T has told me on multiple occassions that she likes the emails because it helps her know how I'm doing in between sessions, and how I'm feeling (since I have a harder time talking about that than emailing about it). It's possible that your T would feel helped in her work with more out of session contact too...