Is a relationship salvageable if one of us were to have cheated on each other and it's known, no longer a secret?

My bf had cheated on me with some random and she considered them engaged even though they weren't, and they wouldn't hangout all the time. Maybe couple times a week. And they had never had sex either. It was just like hanging out when I was busy..

Is it possibly salvageable? Because we have been engaged, secretly, for years now and he really is the one for me... even after his mistake. And it wasn't for a long time. I'm just curious because of how sick I'm becoming over this entire situation.. I haven't eaten, don't sleep, I've thrown up a few times.. and under the circumstances, if people want to tell us she shouldn't be together we plan on possibly just moving far away from where allllll our family is, possibly even across the country... my hearts broken now but if I can get through it without him, why couldn't I get through it and then try again? Obviously not right away!