I would have thought chicken pox if not for the extended time period of 4-6 months you're experiencing this. It could more likely be an allergic reaction to laundry detergent if it's spread across your body, I'd start by changing that to something scent free and hypoallergenic, you can and will develop new allergies at any time over the rest of your life. I became intolerant to dairy very suddenly at 18, I also gained allergies to my cat who I've had for over a decade after 8 years of having her, it can happen for anything.

The cream, allergy pills and shot wouldn't do anything if you continually exposing yourself to the thing you're allergic to like clothing/bedding and towels that are cleaned with the laundry detergent you're allergic to. Outside of allergies this may be a more severe form of acne which can happen later in life, perhaps r/SkincareAddiction would have some answers since they see a lot of skin related issues as well.