I think it's really important for you to go to your session and ask him for help - ask him if he will block your phone number and your email. If you send texts he won't get them and I think emails will just go to a spam folder which her can simply delete. You are doing a great thing by acknowledging you have a problem with self control and telling him you want to stop. Threatening termination isn't helpful to you and it's clear your distressed and want to stop. As your therapist, I think it's his job to at least try to give you some tools to make a change. It is incredibly easy to do and at least keeps him from becoming overwhelmed or feeling violated and it takes very little effort on his part.

From what I've learned and know, any response from the recipient of unwanted texts or emails only serves as a reinforcer for the sender to continue. I've been there on both ends of the situation, not with a T but in other relationships. Completely refusing to engage is the only thing that I have seen work. Just be aware you won't get any responses so you you may get upset and the urges will escalate at first. If your T is firm and consistent, once he stops engaging with you in this way, your urge to do so will subside with time. Perhaps he can let you have his office number so you can leave voicemails if needed, that he can respond to in session.