just because it never showed up you are actually allergic to the food , dosent mean it still wont aggravate or bring out eczema.
well my sister has the same problem too and the drugs she uses are afective only for a short period of time.u must be very selective in what u eat,ur diet can make it better of worst.eating salt and eggplant and tomato .pickles and peper and foods that contain conservative can intensify it,drink much water and ofcourse talk to a dermatologist,maybe new drugs are made or new advise to recive.
The discoloration will go away weeks after each outbreak. .it’s normal 
the best over the counter treatment is cetaphil cream mixed with vaseline, applied all over twice daily.
Most all cats shed and most people with allergies, eczema, asthma would have problems with cats. You should talk to her pediatrician first. My son grew out of the eczema . asthma, but it took him until he was 8.