Same happened to my child, I saved it, it was the smallest tick Id ever seen so knew something was up. CHeck your area, we have a free office that deals w/ mosquitos/ticks, etc - they told me it had been attached 24-36 hours, this is when they start to transmit the disease IF they have it.
Her pediatrician could not do anything right away, as Lyme presents itself only after a couple weeks in bloodwork. I had the tick tested & it was positive for Lyme. Half the ticks in our area are positive. Less than 40% of people who have Lyme get the bulls eye rash, so dont look for that, the flu like/achey symptoms are more indicative.
Once I found out the tick had Lyme I put her on antibiotics. The Dr wouldnt at 1st since that is risky as well, but we ended up doing it. I know you dont have your tick, but maybe your Dr can tell you the risk of meds vs waiting it out. Good luck.