“We’re never so vulnerable than when we trust someone – but paradoxically, if we cannot trust, neither can we find love or joy.” — Walter Anderson
It seems to me there simply isn’t enough trust left in the relationship. You have been hurt and lied to and the engagement ring seems more like a tool for manipulation than a loving gesture. From what you have said he has lied, there is another girl, he is trying to do things to provoke you and he taunts you with an engagement ring – but doesn’t offer it. Do you need this?
The find help tab at the top of the page will help you find a therapist in your area. It sounds like it is time for you to take care of yourself and not be in orbit around him. You deserve more than you say you are getting from this relationship.