mandazzle...
You are not putting her through stress. You have paid her to handle your pain and help you thru a difficult time. You are now offering to pay her double to help you more. It's scary, I know, but think about it in those terms. You aren't being annoying, you are asking for what you need. I'd simply say "I am really struggling right now and I was wondering if you can fit me in for extra sessions until I get better".

It will be okay, your T has heard it before, and she can handle it.