If my boyfriend is allergic to my cat and it's making his eczema really itch, what can we do?

Three options: With allergic diseases there are generally three options: avoidance, medications and allergy vaccine therapy. Avoidance for cats is difficult but one could try a hepa filter system. One should make sure medical therapy is optimized if avoidance is not possible and if not helpful allergy vaccine therapy could be considered.

Treat the eczema: Use otc antihistamines (loratadine in the morning, cetirazine in the evening) and a topical steroid as prescribed by your physician...Or...Get rid of kitty.