Hi, most probably looks like wasp sting. You need to confirm what type of insects is prevalent in your area. With insect bite or sting, symptoms vary from minor bite pain to life threatening anaphylactic shock. The types of manifestations encountered are local reactions, systemic allergic reactions, toxic reactions, and delayed reactions.
According to your history it suggests 'Delayed reactions'. Less than 0.3 percent of insect sting reactions will result in a delayed reaction. It is usually seen 7-10 days post insect stings. It can be associated with the joint pain, fever, hives etc.
You need to undergo important tests like complete blood count which can show neutropenia, with development of reactive, plasmacytoid lymphocytes. Mild thrombocytopenia and Eosinophilia may be present. Measures of non-specific acute phase reactants, including the erythrocyte sedimentation rate and C-reactive protein should be done.
If you are allergic to cat, he should avoid further exposure to it as it can worsen his allergic conditions as the body is already sensitized to the allergens. In his case cross reactivity may exist.
Anti histaminics with appropriate steroid therapy will help to alleviate the symptoms.
I suggest you to consult immunologist/ orthopedic surgeon for detailed evaluation. Take care and regards.
I would not suspect the sting venom as being the cause of the hives almost a week later. The venom should have processed out of his body by that time. I would be much more likely to consider the cat or a change laundry products or soaps/shampoos, maybe even a food allergy than the sting.
You sound like you don't feel the doctor at the urgent care listened to your concerns, but his questions were valid and a frequent cause of such reactions. Consider the posibility at least. Your husband could also have just developed an allergy to the products you have been using. Allergies are very weird things and can seem to come out of no where sometimes.
I hope you get some real answers soon. I am sure your husband is misserable.