It takes 72 hours to transmit lyme disease. More than likely your baby is not in danger of that. Also lyme disease is only carried by Deer ticks. I dont know if they are common in your area or not.
My boys have had ticks with their heads burrowed... totally grosses me out sooooooo much!!! I pulled them out with tweezers then put witch hazel and peroxide on the wound site. It usually scabs up and goes away in a few days.