I wouldn't freak out either, and maybe it's worth doing a little research, but if everyone took antibiotics every time a tick was found on their body, we'd probably have a lot more med-resistant bacteria out there!
Most ticks do not carry lyme disease, and the tick has to be embedded in the skin for 24 hours to transmit the disease according to everything I've ever read. I don't know about other ticks carrying lyme disease. Never heard that, but can't say it's not true. But it is true that the deer tick is so small that you would most likely not see it. It's not invisible, but it's about the size of the period at the end of this sentence.
Certainly if your son develops a bulls-eye rash or fever, achiness, etc. lyme disease would be a prime suspicion. But if not, odds are very low that there is anything wrong. I believe they can do a blood test for lyme disease, but I have no idea how expensive it is.
There's lots of info out there on lyme disease if you do a web search. I know it can be a debilitating disease if not treated early, but fortunately it is quite rare and most ticks will not transmit it to you.