Sodium lauryl sulfate, another name for which is sodium dodecyl sulfate (SDS), is a detergent - meaning it has two sides to the molecule, one side which dissolves in water, and one side which dissolves in fats (such as oil). If you have ever seen oil and vinegar unshaken, you have seen that fats and water do not mix. A detergent allows them to mix, which is why detergents are used to clean. They will allow the oils, grease, and fatty substances that get into clothes and hair to dissolve in water in the shower or washing machine. Detergents are incredibly useful substances, in particular SDS. It would not be possible to make a shampoo or cleaner without a detergent of some type. Detergents should not be taken orally, and I am not aware of any medications that contain SDS.

SDS is very safe, although given any particular substance, there will be a certain population who will react to it. Much like peanuts, the fact that a subset of the population reacts does not make the substance universally unsafe. It is best to avoid any substance that you have a reaction to. Unfortunately, it is challenging when it is to a common substance such as SDS.

Good luck.