As other posters have said, you need to take a closer look at all the cleaning products in your home. Unscented laundry detergent is a start but you also need to nix the fabric softener - they are the worst, worst, worst. Use vinegar where you'd place fabric softener (for the whole family not just baby's clothes - he leans against your shirt, right?). not only will he not have a reaction to vinegar, vinegar helps to remove any soap residue left in the clothes. do a double rinse on all laundry (or at least anything related to baby). also consider trying a different unscented detergent - I cannot tolerate Tide in any form - instant rash. All free and clear works well for our family. Also NO dryer sheets.
My son had mild eczema when he was younger, he still gets it on occasion if we're not vigilant. He does really, really well on California Baby Super sensitive shampoo and body wash. he cannot use anything else except aveeno baby (even children's organic shampoos cause a flare up). eucerin cream (not lotion) was the best for outbreaks.
Green up the rest of your cleaning supplies. best would be to move to vinegar and baking soda for most everything and not use commercial cleaners at all. Remove any plug in air fresheners, don't use a spray either (my son has a horrible reaction to these). no one who comes into your house regularly should be wearing anything with a scent (no perfumes, colognes or overly scented hair sprays, etc). you need to probably look at what is used on your hair and body until you have this under control (i.e., use the same cleansers you use on him or burts bees, etc).
also, this is a systemic reaction - antihistamines are good for getting the reaction under control to start with a clean slate - talk with the doc about the best one to use. for my son, a few days on zyrtec was much better and faster than any topical steriod for getting rid of an outbreak with fewer scarier side effects. hydrocortisone creams are NOT the answer - they will thin the skin with repeated use.
you do need to look at food (although this wasn't my son's trigger). dairy tends to be the big one and I would consider taking him off all dairy for one to two weeks to see if things improve.
you need to be seeing a dermatologist; pediatricians tend to treat the symptoms not the cure the problem.