I gained about 15 pounds in a week. I eat healthily and exercise several times a week. Could 15 pounds really just be water retention?

Strange. It is very unusual to gain that much weight in a week. Not sure what your medical condition is, but if you have congestive heart failure your could certainly gain that much weight in a week in which case you would need to see your doc to have meds adjusted. I would also have a comprehensive blood test to make sure you do not have certain endocrine (hormonal) disorders.
Possible. It is possible to gain weight due to fluid retention- kidney disease, liver disease, heart failure. Please check with your doctor.