Regular bristleworms wont bother you a bit, they're harmless cleaners. But fireworms, well, there's a reason why they're called a fireworm. Their bristles are the things that actually sting you (imagine that...).
But it causes a rash that's rather annoying and lasts for a long time. If you happen to get stung by one you should remove the bristles from your hand, arm, or face. They're tiny and nearly impossible to get out, but you can use something like leg hair wax or tape to help you remove them. Then take Benadryl or something similar to ease the allergic reaction.
Of course if you get hives, have problems breathing, or noticeable swelling call 911 and request an ambulance. There's no sense in passing out while driving considering most people can't operate a car while awake.
But people new to the hobby are often scared by the things in their live rock. Yes they're a lot of scary things that could be in your live rock, but don't let that ruin the fun of the hobby. But when you bring home a blue ring, then you can worry about your tank.