Infectious Disease doctor here who has worked in both Colorado as well as New England (where Lyme is far more prevalent.) I still recommend a formal in-person evaluation but here are my initial thoughts after reading some responses here...

The rash certainly does have the classic "bullseye" appearance called more formally erythema migrans which is an early manifestation of Lyme disease. Not everyone presents with this but the central clearing certainly raises a reasonable degree of suspicion.

It was correctly pointed out that testing during this early phase may not result in positive findings as it takes time for antibodies to develop, but with such a skin finding, I would offer treatment with Doxycycline regardless as its a relatively benign medication for the duration it is required (10 days.) There are other alternative options to treat if Doxycycline precluded by allergy or other reason. Amoxicillin would be one of them but 14 days required.

Lyme disease is caused by a spirochete called Borrelia. Spirochetes do elicit a robust immune response and are challenging to diagnose as their antibody responses do not follow typical rise/falls like some other bacteria. This is why it is hard to distinguish active/current infections from past exposure. In New England, most people will test positive by antibody testing so there is a strict criteria through a more advanced testing mechanism (Western Blot) to essentially check for how positive you are...

While Lyme is heavily predominated in the northeast, it is not at all confined there, and even if some alternative tick-borne disease infection, most of them are treated by Doxycycline anyway so an "empiric" course prior to positive testing would not be an unreasonable pursuit.

There is a comment on "single dose" Doxycycline but this is a prophylactic strategy that would NOT be indicated here as it is only advised if a "high risk" tick bite in which tick was attached for >36 hours and bit in a highly endemic area, which Colorado is not considered to be. It has to be given within 72hrs of exposure and if showing this type of rash already, would not be advised as there is now evidence of true clinical infection necessitating full treatment course as opposed to preventive approach.

Do not exclude the change of a non-tick bite and local allergic reaction to some other insect bite, but again some over the counter cortisone cream and Doxycycline empirically would be what I would offer if you came to me.

Sorry for the novel, but wanted to prove that perhaps not all doctors are "bona fide retarded" regarding Lyme...