Mucinex will not stop your period. In fact, I don't know of any medication that will - other than hormonal medication (birth control pills). If you know there is no possible way you could be pregnant, then it isn't that. Stress can cause you to miss your period. Weight loss. No ovulation can prevent you from having your period.
Don't think of the worst possible situation first - think of the easy things (not that stress is easy).
Go see your doctor as soon as you get coverage.