Don't hurry to the doctor! There is nothing they can do. My clinic won't test immediately after a bite because it won't show up. Watch for symptoms, especially a rash anywhere on the body and fever. And know that the test is not always accurate, so if you think your lo has it and the test is negative, you can still push for the antibiotics. I am pretty much against the use of pharmaceutical drugs unless it is absolutely necessary, but I would not hesitate to start antibiotics for myself or my children if I suspected Lyme. It can be really awful, and it's best to treat it right away.
We have a lot of Lyme in the area where I live. We found 2 ticks biting dd yesterday, after a long weekend outside. I check myself and my kids daily, but sometimes they get missed. I do as Elil's mom said and immediately put tea tree oil on the bite when I remove the tick.
I'm not sure if you do regular visits to tick-y areas, but if you have a dog, putting a systemic flea and tick killer on them can really help with the ticks getting on the people in the house. I know, it's poison and probably not very good for the dog, and I would not put it on myself or my children, but with half of my family suffering from Lyme and its complications, our dogs have to have it if they want to live in our home.
When you go out, it really helps to tuck your pants into your socks because the ticks will crawl up the inside of your clothing. Also, tuck in your shirt and wear a hat. When you get home, strip down, put the clothes rigth into the washer and wash them, check your shoes and your bodies for ticks. Check again in a couple hours -- they are sneaky.
Hope that helps. Don't worry, just be vigilant and think positively! Your lo probably didn't get Lyme from that tick.