Depends on duration. Have you had this all your life, or just recently? Is it associated with a different place to shower? Do you wheeze? Do you get dizzy? Do you get chest pain? Best to ask your doctor to check you out.
Asthma or CHF. Asthma or even congestive heart failure (CHF) may explain shortness of breath (sob) when showering. I will assume that there are no hives on your body when you shower because a rare disease involves cold or heat induced hives and anaphylaxis which could cause sob. I recommend you get a breathing test and maybe an ekg to check on your lungs and heart.