While it is not common, some people find that they get skin rashes or welts after handling their hedgehog. In general, hedgehogs are considered to be low dander and have been recommended as pets for people with allergies as they don't shed dander in a way that tends to trigger wheezing, sneezing, or watery eyes. Fairley, Suchniak, and Paller (1999) examined three case studies and reviewed literature, and came to a conclusion that there are several likely reasons for skin reactions to hedgehog handling:
1) When you get pricked by a hedgehog, dander can get under your skin. It has been found that people who have allergic reactions to cats are likely to have an allergic reaction to hedgehog dander. In this condition, there is generally no reaction to the hedgehog unless prickled. So, if you are allergic to cats, you will want a hedgehog that is calm and generally doesn't raise its prickles, and to be cautious if handling a hedgehog whose prickles are up.
2) Hedgehogs tend to self-anoint (lick on the smell, then spread it on themselves with their tongue) when they come across new smells in their environment. People have been allergic to things the hedgehog anointed with, but not to the hedgehog itself. A commonly reported reaction is to pine shavings. If you are allergic to pine, it's best to pick a different kind of bedding.
3) Some hedgehogs can carry fungal infections without showing any symptoms. In these cases, reactions are highly inflammatory, but resolve within 2 to 3 weeks of onset. I have never personally heard of anyone having this kind of reaction.
If you are having a reaction to handling your hedgehog, you will want to pay attention to what your hedgehog may have on its quills to see if you can make environmental changes. You may also need to use gloves or a hedgebag for handling. If reactions are severe or persistent, definitely talk with your doctor.
