Ok, the early pics look very much like an em rash to me, but I think the ring usually expands over the course of a week or so. The fact that the ring went away so quickly, I think that suggests that it is not a borrelia infection and that it is most likely an allergic reaction. Quoting saraeli from above: "I get bullseyes from fleas because I am allergic to them".
On top of that, its looking much more like a mosquito bite now as you have said. Transmission of Lyme by mosquito is considered highly improbable (maybe impossible).
i think this is good input
the EM rash typically expands for several days or longer after first appearing and as above is typically present for much longer and grows much larger than the photos show - whereas immune reactions to mosquitos are common and typically form a hot itchy bump that fades after a day or so
the EM rash is typically flat or v slightly raised around the edges - and does not typically itch much
a tough call - as weighting v small risk of infection with high risk of consequences / vs some risk of self treating such a young baby with abx
astragalus may be a safer option that may offer some protection - as far as i can tell it is used for children as young as 18 months or less
another secondary option would be to get a private blood test to check for antibodies - but this will not be useful for another few weeks ( i think 4-6weeks after exposure) - and the testing also lacks sensitivity - perhaps even more so in babies who's immune systems have not yet matured
-a positive test would suggest treating aggressively - but this would be later than ideal
-a negative test cannot be interpreted to mean very much unfortunately - due to the poor sensitivity
so this option is far from ideal
other than that you can look for any symptoms onset - typical symptoms at onset include - flue like symptoms, noise and light sensitivity, neck pain, headaches, fatigue etc - but some of which is hard to know in an infant as they cant tell you about
overall if it is not still growing - it seems unlikely to be an EM rash and therefore unlikely to be a sign of lyme