Listen, it's not okay at all that your boyfriend has threatened to kill himself in the past when you have tried to end the relationship. No doubt, he needs help and you alone cannot fix him and shouldn't be responsible for doing so.

That being said, you are not innocent. I have no respect for cheaters, personally. I see zero excuse for it whatsoever. Even in this post. So yes. You need to break up with your boyfriend properly if you are going to move onto a romantic relationship with this other person. You are cheating on your boyfriend and he doesn't deserve that, just like you don't deserve to be trapped in a relationship out of the fear of him ending his life.