I know plenty of people who have had lyme and most have been lucky to catch it early. I know of one woman here in WI that was misdiagnosed with MS I believe, when she actually was suffering from severe lyme disease. It took a few years to get a correct diagnosis.
By all means strip your clothes off and check for ticks, even if you and your clothes are treated against bugs. Personally I think it's just a matter of time before bugs build up an immunity to what people are using, hopefully I'm wrong. Removing the bug before it has a chance to dig itself in is crucial. I am regularly dropping trow right at parking areas to check myself over and encourage anybody who is with me to do the same so you can surely do it in a camp site. Tuck your pants into your socks, check yourself every few minutes as you walk, wear bug spray, drop your pants and take off your shirt to check for ticks that have made it through the other defenses, try to not walk in tall grass and brush during the worst parts of the season, etc.
In my experience ticks are at their worst in spring and fall. It must be that the little ones are freshly hatched and looking for a host and then the pressure drops some in the drier months and picks up again in the wetter fall but not near as bad as in the spring.