I was just prescribed this liquid called magic mouthwash. What happens if I swallow it?

Yes. Magic mouthwash has several different formulations which are made up at your pharmacy. I would ask either your dentist or pharmacist, but with most of the formulations you can swallow it.
Nothing probably. The magic mouthwash that i prescribe is supposed to be swallowed. You need to consult with your dentist to see if your formulation is supposed to be swallowed. If it's the same or similar to what i prescribe, it should be ok, but please check with your dentist.