You need to set boundaries with him. Did your T could set up a goal focusing on the therapeutic treatment required for you to overcome the depression?

The dilemma is what you feel about keeping a relationship with him and your bf not being able to cope with your mental illness.

The trust thing is difficult to deal with and if he has had plenty of time to accept the situation what you have posted, then you need to discuss the whole things and what needs to be done to be acceptable to both parties. That is why I would prefer you work with your T as your T has had sessions with you. This is important to find the best option for you.