It's very difficult. Hopefully, your program will understand and allow you to swap work shifts / calls / etc. They absolutely do not have to give you the time off. If they don't, and you go anyway and don't show up to work, you risk getting fired immediately.
Hopefully, some creative swaps and/or vacation time use will help. Or, perhaps you will get a prematch offer and only require a few interview days. Or, your home program will offer you a spot.