What you posted sounds exactly the same as what happened to my son Braden at about 8- 81/2 months! He first broke out in some sort of bumpy red rash that spread to his entire body. They thought he had some sort of infection but we never found out what kind. Anyway, after his bout on antibiotics he started drying out really bad and then started peeling from head to toe, even the palms and soles. It was very weird but his skin looked so wonderful after about a week of peeling. The only thing that got worse was his scalp - during this whole process his scalp got really scaly and that had not been the case prior to the rash, anyway -the scalp now is the worst part of his body.
The peeling was probably a little over a month ago and the thickness is now starting to come back. I also remember at about age 2 months he had a similar peeling experience but his skin had not started thickening up so it was not as noticeable. I am seeing a new pediatric derm today and I will bring it up to see if he has any explanation. If I find out anything new I will let you all know.