If it were me I'd actually look to STOP using moisturizer, I'd think of it the same way as the soap as I know I get plenty of other skin reactions to all sorts of products. It gets worse the older I get it seems.
Personally I'd also be looking into the foods I eat, as I have celiac disease and I seem to get itchy without getting a full-blown dermatitis herpetiformis rash that can go along with the disease. Yes that's really specific to me, but it's possibly you're reacting not to an external irritant, but a food.
I wonder if bendryl would even help the itch if it were due to poor liver function? Does anyone know? It will help if you're getting a histaminergic reaction (ie: a standard allergic reaction.) If it's another sort of immune system reaction it can also help, although you will find some doctors saying it won't. (I've read such things on a celiac forum I frequent, as celiac disease is an autoimmune disorder but not an allergic reaction.)
That you're saying taking it helps, however, implies to me that it's some environmental thing setting off your body that you can hopefully pinpoint and get rid of. That this sort of thing can be a symptom of ASD doesn't negate what I just said either...there's lots of weird medical things that are as yet to be understood in regards to ASD, things that don't specifically pertain to the brain.
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Not autistic, I think
Prone to depression
Have celiac disease
Poor motivation