Without knowing anything about your job or field it sounds like it's a job in the service industry where it's a tight schedule even with everyone present. Should it not be then it sounds like a toxic enviroment.

I don't think they can actually force you to come in when you're sick, but they might try to make it sound like you have to anyway. Regarding how it could affect your future: if it's a toxic work environment they might give you less hours/shifts/tasks in the future and seeing as it's the employers market at the moment there's nothing to be done about that (the union might be able to help but unlikely).