Most likely your laundry detergent in your sheets. What u describe sounds like urticaria a.k.a. Hives which are typically seen with allergic reactions.
Did u change your laundry soap or softener recently. Are these new sheets, maybe you are allergic to the material tge sheet is made from.
do they come and go or just spread? flat red splotches? raised? any fluid?
does it look like a rash or a scratch or a bite or blisters. what do you mean by welt?