Two things right off the bat. First, shrugs aren't a compound exercise. Secondly, that's a terrible plan. There are tons of effective routines that can still be done with under an hour per workout.
This could be anything, from a slight sprain to a serious tear. I'd definitely find a way to get checked out by a professional.
Since you don't know what's wrong, you have no guarantee whatsoever that it'll heal, or even begin to improve, in a month.
You're a young dude. Remember that you've got 50 or 60 years of training ahead of you. Taking even a few months right now to stay healthy and do prehab/rehab (if necessary) would be a small step in the big scheme of things.
Or... you can ignore it and possibly become a 25-year old lifter who constantly complains about his nagging shoulder injury that flares up and prevents him from doing even more effective training.
No, not right.