I was actually reading about allergies in "The Hive and The Honeybee" a couple of nights ago.
In the chapter the chemical make up of venom from stinging insects is discussed. The venom from honeybees, yellow jackets, and ants each have a different chemical composition. It would definetely be possible to be allergic to yellow jackets but not honey bees.
The chapter also discusses how allergies develop. For an allergy to develop a person must be stung twice by the same insect at two different times. The first time someone is stung, they will not show an allergic reaction. But the body will build up antibodies to the venom. Later when the person is stung again an allergic reaction could occur.
As has been mentioned reactions such as swelling, burning and itching near the sting site are normal. But if rashes, swelling, burning and itching occurr remote from the sting site, this is an allergic reaction.