I feel your pain. I was there about six years ago. I was shooting a finger release, & when the pin hit the target, the release was punched. It was sort of like a drive by shooting. I went to an archery shop & bought a pure back tension release.(best $50 I ever spent) I hooked it on,drew back, tried to hammer it, but there was nothing to punch. After drawing & trying to hurry my shot two times, I could start to relax & pull through the shot. Since then I've shot only thumb releases, which I can shoot like a back tension release. It wasn't cured that quickly, but I was shooting 85-90% better in the first week.
There's a book by Bernie Pellerite called "Idiot Proof Archery" that I highly recommend. It covers all phases of archery, & explains the different forms of target panic & how to cure it.
One thing to try is to keep your finger/thumb away from the trigger & just draw,aim, & let down for a while. If a bullseye still bothers you, try aiming at a blank target until you start to relax.