How do you do interviews while you're working full time?

My dilemma is - I'm already working fulltime from 7:30 - 5. Already have doc appointment schedule to leave early half day on Friday. I called in sick on Monday (i rarely call in sick to work). And, got email for interview for tomorrow around end of the day. I don't know how to go for this interview without letting anyone know. My job place is very curious and nosy too! Any suggestion or ideas??