at any age can be very distressing. Since you are young, and you do not have a clearly defined family history of hair loss, then you should probably be seen by a specialist. In this case the best type of physician for you to see is a dermatologist
Hairline receding at the corners is most consistent with androgenic alopecia (also known as male pattern baldness). Although it usually starts later in life, it is not unheard of for it to start at your age. Sodium laurel sulfate is a detergent found in some shampoos and toothpaste. It can be irritating to the skin and cause rashes, but has not been shown to cause hair loss. If you are really worried about this ingredient, you can try using a soap without it.
There are treatments for androgenic alopecia if that is what you end up having. The first line treatment is a drug called finasteride (also known as Propecia). It has been shown to halt hair loss for at least a year in around 80% of men with male pattern baldness. Second line treatment is a topical drug called minoxidil (Rogaine) which can be effective as well. The dermatologist you see will be able to go over the details of these options with you.