Is trimethoprim sulfamethoxazole likely to cause hives?

As likely as any. Trimethoprim sulfamethoxazole (septra (sulfamethoxazole and trimethoprim) or bactrim) is an antibiotic used for urinary, respiratory and middle ear infections. Its use has increased because it is effective against many strains of MRSA (methicillin-resistant staph aureus). Like other drugs taken intermittently it can trigger allergic reactions. Hives are a common symptom of allergic reactions to drugs.
BACTRIM (sulfamethoxazole and trimethoprim) AND HIVES. Trimethoprim sulfamethoxazole is a sulfa drug. The trade name is either Bactrim (sulfamethoxazole and trimethoprim) or septra. These are the drugs that probably cause hives more than any other medication. Stop immediately!