You aren’t doomed, but you need to change the way you present your situation. You make it sound like you are the victim. You ‘let a friend borrow your work’ and told him not to copy. That was cheating. Tutoring your friend would have been fine. That’s not what you did. If you continue to present yourself as the victim, you are unlikely to gain any sympathy from a grad school. (Or from the honor council to which you appealed.)
It’s better to own up to having make a mistake. I don’t know if there is a cultural issue here. Your English suggests that it’s not your first language and I’m assuming you could come from a country/culture where it’s routine that students share their work and it’s not considered cheating (to give this the most generous possible interpretation.) Own the mistake - that this is considered cheating here - and that now that you understand that, it won’t happen ever again.
People make mistakes and many are given a second chance if they have an otherwise stellar record which it sounds like you do and they acknowledge their error. Are you certain that transferring is the right course of action here? If you have faculty who understand that this was a one-time mistake because you didn’t understand the seriousness of what you did, perhaps they can advocate for you at the graduate level.