Hives are normally caused by a substance that's taken internally into the body. I, for instance, am allergic to strawberries and penicillin both of which cause hives on my body and cause breathing problems for me. I am also allergic to timothy grass and mold neither of which causes a rash. My husband is allergic to cats and they don't cause a rash or hives, but do cause an asthma attack.
If pets don't usually cause her to have a rash or hives, then I would get to the Dr. immediately. It may be something else that she's eaten or taken that's causing this type of reaction. If so, her throat can swell mimicking an asthma attack and close off so she can't breathe.