"Patch like rashes on his legs and arms" sounds like eczema to me. I personally think eczema is an environmental disorder because I have eczema real bad on my hands and when I went to West Virginia for a week on business, my eczema went away completely. When I got back home, it was back within a week. It must be something in the water, something with my diet that was different when I was traveling, or something in the air that's regional. It's definitely an allergy of some sort, but my dermatologist says they don't know what causes eczema for sure. While it can be treated with moisturizers and topical steroid creams, there's no cure.
If it's prickly heat, there's really nothing you can do but wait it out. My son has had problems with prickly heat since a very young age. On my son, it would usually go away after one or two days though.
If it's eczema, you just have to keep it moisturized and if it gets worse, they do have steroid creams they can prescribe, but it usually does come back even after being treated. My son has the patchy rashes on his legs right now and I put Eucerine or Cetaphil on them at each diaper change and when they start to get so bad he's really scratching them, I put the steroid cream on them for a few days and they go away. But again, they always seem to come back. My daughter's dermatologist said to use a non-soap cleanser when bathing to help revlieve the eczema. She recommended Cetaphil or even Dove bar soap is better than Ivory because it has moisturizing cream and ivory is pure soap. With your son being so young, the doctors may not want to use steroid creams on him yet so using a good moisturizer and non-soap cleanser when bathing would probably be the way to go until he gets older. I know you said the lotions you tried made it worse, but did it actually spread or did it just seem more red than before? When I put the cream on my son's legs, it does look more red, but after several days, the rash does seem to disipate so you just may need to give the moisturizer a little more time.
Another mom I know who's real into all the "natural" remedies for stuff told me she thought eczema was caused by the lack of essential fatty acids and recommended a EFA supplement. She also recommended adding filters to all my water faucets. She said you can buy one for the shower and bathtub as well as the kitchen and bathroom faucets. I'd take her advice on the water filters except my husband works for the city's water department and he thinks that's rediculous.
Anyway, you might just try some different non-soap cleansers, a good emolient moisturizing cream (not necessarily lotion) like Eucerine, Aquaphor or Cetaphil and maybe filtered water in his bath and see if that doesn't help. And if you do try filtered water, and it seems to work, please let me know. I need ammunition to get my husband to change his mind about adding filters around here. :-)
Good luck!