I've had fish poisoning before, I stabbed my thumb about 40 times with hooks baiting up for a halibut trip, and we were on the water so no option of going to the doctor. My entire hand puffed up and turned red. I soaked it in warm hypersaline water I made w/ rock salt. It helped disinfect it and the swelling went away. If you have peroxide, or iodine handy next time you cut yourself both of those are good options.
Here is some good info about treating finger infections:
http://www.emedicinehealth.com/finger_infection/article_em.htm
There are horror stories, but in the majority of cases you will be dealing with an infection and not a reaction to an animals nematocysts. The only animal in our tanks that we REALLY need to watch out for are zoanthids/palythoas. Those carry a potent neurotoxin that can wipe you out if introduced into your mucous membranes or bloodstream. Also watch out for your pets, as I recall a story on reefcentral about a dog that drank from a zooanthid frag bowl and died.
Here's a good source for info, and the dog story is included as a sublink:
http://www.reefcentral.com/forums/showthread.php?t=158730
Anenomes have also been reported to have a sting that is strong enough to be felt, but I haven't heard of any cases of actual injury. However, during one of Dr. Ron Shimek's talks he mentioned a case where a person who kept anenomes had developed a reaction to the frequent exposure to their nematocysts in the tank water. He claimed it got so bad that this person, who initially had not had any problems, began having swelling and redness from simply reaching in their tank. Anecdotal, and I can't find sources, but I thought it might be interesting.
I do also have personal experience with a case of jellyfish allergy. I crabbed with a guy who's face would puff up until his eyes swelled shut every time we went through a patch of jellyfish. The line gets coated with their slime, and it sprays everywhere when the line goes through the block. For most people, this is merely annoying because it stings your eyes, and to a lesser degree your skin. This guy would puff up fast, right after contact. However, I think someone would know quite quickly if they were allergic to their reef tank, and I would also think that this condition could be treated with normal allery medication such as benadryl.
Hope that helps,
-Gusty