Scaly patches that itch sound like excema. I have had it all my life, and it is indeed an allergic reaction -triggered by exposure to a substance my skin doesn't like, usually a detergent. Once I am exposed to a trigger it takes a long time to get the rash healed & other stuff that didn't bother me before can aggravate the exisiting patch.
It can't hurt to look for internal triggers as well, so I would agree it's worth checking your diet.
The first thing is to stop using the product, which you are doing - you might also switch to the mildest detergent you can get for the diapers & clothing. Charlie's soap is additive-free & works well for diapers.
I'd stop the baby wash & lotion as well for now... my babes have my sensitive skin so I just use warm water on them and if there's a big mess, bathe them with a tiny bit of handmade castile soap.
The other big thing that helps is to keep the area dry, hard to do when it's diaper area but after each change give him lots of nekkie time.
On acute breakouts, I use unrefined shea butter - it takes away the pain and redness & softens the scales so they aren't so itchy. I get it at agbangakarite.com, their stuff is very good quality & has always been effective for me.