A friend of mine recently got a rash (I don't think it was a classic bullseye pattern) and some fatigue. She didn't notice a tick. Went to a doctor, suggested that it might be Lyme disease -- doctor told her if she'd had a tick, she would have noticed it, so it must be allergy. A month later she was in the hospital with a confirmed Lyme diagnosis.

If I get an unexplained rash with flu-like symptoms, even if I don't see a tick, I'm taking antibiotics just in case. Better safe than sorry.