Hi,
This does seem to be an allergic reaction to Bactrim.The most common adverse effects are gastrointestinal disturbances (nausea, vomiting, anorexia) and allergic skin reactions (such as rash and urticaria).
What you have described sounds typically like hives.Hives are raised, often itchy, red welts on the surface of the skin. They are usually an allergic reaction to food or medicine.
When you have an allergic reaction to a substance, histamine and other chemicals are released into your bloodstream, causing itching, swelling, and other symptoms.
Treatment may not be needed if the hives are mild. They may disappear on their own. You can take antihistamines like Cetrizine though it causes drowsiness, Loratidine is a better drug but it will take 2 days for it to be effective in treating the condition.
Apply Calamine lotion on the areas to relieve the itchy feeling.
ref:http://www.myonlinewellness.com/topic/adam1000845
I think it could be a reaction you should ask your doctor because it sounds like you are allergic