Last but not least, you may be allergic to cats if you develop a rash or break out in hives, especially where a cat has licked, scratched or bitten you. This is one good way, in fact, to narrow down what is causing your immune system to go into overdrive. It may not be entirely the cat's fault (cats can shuttle around lots of other allergens, especially if they're indoor/outdoor), but you've got a pretty good case if you witness direct evidence. A cat scratch -- easy enough to acquire! -- followed by skin irritation could very well equal a pet allergy.
If the allergic reaction is irritating or debilitating enough, visit a doctor to get an allergy test and specific advice on how to go forward. You may need to find a new home for your pet, but hopefully by practicing some of the management techniques we've discussed, you'll be able to mitigate any allergies your family suffers from.