Which one will give me faster results?

Definitely throat swab. It's cheaper, less painful, and usually they swab your throat and in 15 minutes or less they have the result. I don't even know if they do blood tests for mono. Also, if it's strep, a throat swab will tell you that too. They just look at the culture under a microscope to determine it. Either way, your doctor will probably prescribe you antibiotics or some other medication if you are leaving town.