3 baths in one week is a whole lot. I only give my dogs baths once in a while. It may be too many baths is drying his skin out. I hope you are using doggie shampoo and washing it out well. Cause the shampoo can make him itchy too.
I'm no expert but my dog was itchy and I was freaking out about fleas searching through her long coat every morning trying to catch one lol, but about 3 weeks later she wasn't itching as often anymore and I figured it could of been mites as she had just had a immunisation shot at the time, and my understanding of mites is that they are controlled by the dogs immune system. So I figured meh immunisation shot, give it a bit of time and keep an eye on her skin.
The itching could have been from just one flea bite or it can be from an allergy to food or environment. I would think as someone else mentioned that the 3 baths would make the skin dryer. Hope that your little guy gets some relief from the itching if not a vet visit might be necessary.
My boy was seen by my breeders vet and had his first round of vaccines with her. But I still took him to my vet the first week he was with us to get him weighed, stool check (to check for worms) and just a overall exam. I wanted my vet to look him over. We also discussed what his vaccines schedule would look like moving forward. I would recommend taking him
The itching....could be several things. I would not bath him anymore you could be drying his skin out. Are you sure you are rinsing him well?