Hi Thimble.
It is a really tricky situation you are in. If it were me, I would accept the money offered from your friend, and then talk about it with your therapist about why you are uncomfortable accepting help. My guess is that your uncomfortableness accepting help also impacts other parts of your life. Hopefully with therapy you would be able to get financially stable enough to cover what your friend is paying for. The only thing I would want to do in this situation is set up a plan with your friend about how long this is going to go on for. Like are you going to have this set up for three or six or nine months before reevaluating. I would feel uncomfortable accepting help like that on an open ended basis. Hopefully your treatment would help you be able to get a job that would help to pay for therapy. The other option that I just thought of is if there is a university around you with a psychology department graduate program, a lot of them provide therapy by their students (some of it long term) at a very reduced price. (My school has sessions for $10.) You are being treated by someone who is in training, but they are supervised by clinical psychologists.