I don't think your rash is an EM rash but it's good that you are on Doxy and Gary gave you great advice on how to take the Doxy.
I read that it doesn't matter how long a tick is attached, it could take seconds for a tick to inject the bacteria into one's body and most people don't even feel it because ticks have a numbing agent. Also, most people never even see the tick or any blood sucking vector that carries lyme bacteria as the "host" of most lyme bacteria is the "white footed mouse".
Anyway, here are some photo's and information:
Hope this helps and hope you don't have lyme. Please keep a log of any symptoms you may develop or have every day just to be on the safe side and next time you take photographs, place a coin or ruler next to the rash along with the date, again, just to be on the safe side.
Hope this helps,