It is hard to move on while grieving, if you can compartmentalize your studies (it's kind of like putting the pain in closet, or box for a while and "forgetting") and grief for a time (not that you won't have spill-overs) I think you can both succeed and grieve...even set aside time to grieve... Some mindfulness exercises/or other physical activities (running, walking, swimming, whatever is available) can also help. Sometimes, work can be the way through the worst of our grief...
Keep putting one foot in front of the other...I am so sorry you are going through this, you Really did Not do Anything Wrong! This is someone you had a life with, who was a part of you (and at some level will always remain a part of you)---I have two friends very happily married to each other (not without struggles we all face) --they were each previously married and the woman did have sexual intercourse with her ex once during the time she was getting divorced and planning to marry her love...it was tough on both of them but he and she both understood it for what it was...a moment of weakness, a moment of lost intimacy returning, a mistake, a human mistake, not worth beating anyone up over. (they have been together many years now, with grown children etal)