Maybe it isn’t the cat causing your allergy. It could be your houseplants.
Any house plant can cause allergic reactions but Ficus ( weeping fig aka Benjamin’s fig ) is the most common. The milky sap on the leaves is the cause. The sap gets attached to dust particles and dispersed through out the home or office. People with latex allergies are most likely to react to ficus.
Other plants known to be a problem are chrysanthemums and daisies. Of course any blooming plant or scented plant can cause reactions.
Then there is the problem of mold in the potting mix of house plants to be considered.