It sounds like you may be describing exercise-induced hives
. Hives are welts that are raised and red and that can develop anywhere on the body; they are often intensely itchy and they should respond to an antihistamine, just as you have described.
Exercise-induced hives or exercise-induced urticaria (the medical term) is an uncommon but generally benign condition. Often people who have exercise induced urticaria will have generally sensitive skin and a tendency to develop hives in other situations as well. For example, if you scratch your skin under other conditions than exercise, do you also get the hives?
Luckily the treatment for exercise induced hives is to take an antihistamine before exercise just as you are already doing. It is best to take a nonsedating antihistamine such as loratidine (Claritin) or cetirizine (Zyrtec), and you could take this every day or just as needed. You should talk to your primary care doctor
about this as well, however, to confirm the diagnosis and confirm that no further workup is needed.
Rarely, people with hives in this situation are predisposed to a rare condition where exercise causing their face to swell and their airways to close off. This can be life-threatening, and if you were ever to feel like you couldn't breathe or you had swelling of the face with exercise you should call an ambulance or get to the emergency room.