How to miss work for an interview?

Thank you in advance! I'm in a bit of a predicament!

So I hate my job, but I suck it up and go everyday, whilst actively pursuing employment elsewhere. Today I got a voicemail from a job that I think would be a great fit for me, and it's 3 hours away from where I live (I'm willing to move). I will be calling them back tomorrow, and I'm guessing they might ask to schedule an interview, which means I need an excuse to get out of work that day to make the 3 hour drive. The problem is, this week I was sick with something awful, missing a day of work and getting sent home early the next, so I can't really call out sick again as an excuse. Any ideas how I can swing going to an interview without hurting my reputation with my current boss?

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