What detergent are you using to wash your clothes and sheets? Do you wash your sheets AT LEAST every two weeks? Also, are you rinsing your laundry twice to get rid of the soap, not just the once the machine usually does?
Do you have a good quality filter on your showerhead? (Even better would be a whole house filtration system. I'd love to filter all our water, but those are expensive and nearly impossible to incorporate in a rented apartment.)