My DS is allergic to dairy, soy and peanuts (confirmed by blood test). And it appears that he may also be intolerant to salicylates, so we're both on a very restricted diet at the moment, as I'm still breast-feeding. His eczema still flares up at times, but his face would flare up really red and angry at the end of each day, and settle down again overnight, which has stopped. The only fruit he can have at the moment is pear, he doesn't like bananas, and only tinned pear at that, which has to be in syrup because the juice contains salicylates. I haven't been able to try fresh pear, as it needs to be very ripe and thickly peeled, and at the moment pears start going off before they get ripe enough to give him! Potatoes also need to be old, and thickly peeled to get them low salicylate, maybe it could be something like that? I'm clutching at straws (and speaking from my own experience), also agree with PP's about holding off on any further introduction of solids until you can see someone.
If you do decide to try rice, I'd get ground rice from the flour aisle to make rice porridge with, rather than using one of the baby cereals, just because of what else they can contain which he might react to.