Sounds EXACTLY like my son. He is allergic to fragrance, and when he gets warm at night (sweats even a tiny bit) the sheets would make his eczema flare up severely. I had to switch to hypoallergenic detergent, eliminate fabric softener completely (it stays in the machine up to four loads later) and wash everything in the house over to get rid of the scent. You don't need to buy any of the mom-who-works-at-home-selling-shaklee/arborne anything, there are perfectly fine brands in the supermarket.
I had to be vigilant about MIL "helping" with laundry when she watched my son ever, she without fail would find the old stuff, which she thought smelled better. Yes, it smells nice, but it will aggravate his skin. I ended up having to get it all out of the house.
So, now we still use the hypoallergenic stuff, and rinse twice, and his skin is mostly under control. Rarely, he will get a flare up. I did have to limit my dairy, but it was mostly the laundry. Try that before you switch him to formula, I think you might be glad you did. Butter him up good with some lanisoh (nipple cream), use aveeno oatmeal in an ocassional bath (overwashing will flare it too, use a washcloth to wipe him down) eliminate using scented baby wipes all over him, etc. I think you might find this works, and you can keep giving you baby what nature intended. If you want more answers to what worked for us, contact me privately, I would be happy to help, it made such a difference to my son, his was very severe.
Good luck
D.