I had chronic lyme when I got pregnant with my daughter. She is 23 months now and in perfect health. I had her tested when she was born and again at 1 year with a western blot just to be safe. From my lyme specialist, and high risk pregnancy ob/gyn, the risk they told me of passing lyme was small. Yes, it can be passed from mother to fetus, but the risk they told me anyway, was low.
I wouldn't stress over it too much. Watch your baby and look for signs and it is always good to test to give you peace of mind, but no, I wouldn't give (and can't imagine any dr doing so) an infant antiotics without cause for them.
I don't worry at all anymore that my daughter could possibly have lyme. If I ever see any signs, I will jump on it, but she is a perfectly happy, healthy litlte girl and she too was jaundice at birth. That is very common and not lyme related.
I was diagnosed in 1998 by the way and my daughter was born in 2008.