Got any vacation time saved up????
It's flu season. Call in sick.
Never quit one job before you have another. BIG risk. However, never treat you current employer dishonestly in order to go 'interview' with the potential employer. If your current employer finds out, it is grounds for termination. If your potential employer finds out, it is grounds to not offer or retract an offer for new employment.
Be straight up and honest. Use your time (vacation, personal) to take care of stuff like this. That is why you have it.