Hi M.! My 4 yr. old was born at 27 weeks, 1 lb. 4 oz. and we struggled with weight up until about a year ago. She is now 50th percentile for both height and weight, but more important than that, she is healthy and developing normally. We saw a nutritionist in the Pediatric dept. at UMass and found her to be very helpful in identifying healthy foods that provided the "biggest bang for the buck" (avocado, bananas, coconut milk, etc.) and in sneaking in extra calories here and there (jelly, ketchup, dressing whenever possible). For us, parmasean cheese on everything worked, but I'm sure she'd have some great ideas specific to the allergies you're dealing with. I'm happy to share her name and contact info with you if you are interested. Have you talked with anyone at Whole Foods or the like? Many of their employees are pretty well-versed in allergies and specific dietary issues.
We put Duocal (a "tasteless" powder of concentrated carbs and fat) on anything and everything. I mixed it with breast milk, juice, cereal, spaghetti, homemade baked goods, anything moist. We called it "magic sprinkles." You can buy it at the pharmacy without a prescription for about $25-$30/can, but you can also try to get your allergist or pediatrician to write a prescription for it so you would only have to pay your insurance co-pay.
As for only eating hot dogs, eating one or two foods exclusively is pretty common. Hot dogs aside, your son is getting the nutrition he needs from you. You could look at the hot dogs as simply bonus calories and fat. I would imagine, too, that anything you would normally make with milk, you could make with expressed breast milk. Pudding? Add some Duocal... tasty and loaded with calories and nutrition!
Lastly, I read parts of "Child of Mine: Feeding with Love and Good Sense" by Ellyn Satter (recommended by the nutritionist) and found it helpful in putting my mind at ease. I know how anxious we were about every ounce our daughter gained or lost and consequently about every bite she took or refused. Try to trust that he's getting what he needs from you and that you are doing a remarkable job providing for and nurturing him!