K.B.
I would see a pediatric allergist. I don't know what ALCAT is. I'd recommend either a blood test (RAST is the one I've heard of) or a skin prick test. A blood test can test for a lot of allergens at once, but takes a couple days to get results. A skin prick test requires testing each allergen on the back of the child with each thing you want to test, but the results are read within 15 minutes or so of doing the test. Or, since it seems triggered by food, you could do a skin prick test for the common food allergens and then get the blood test for a more extensive testing of other allergens. That way you'd know right away which foods you should be avoiding. And you can also get an epi-pen prescription if it is a food (like nuts) that could be really bad.
The sleeping flair ups could be delayed reactions to the foods or it could be a dust mite type allergy, particularly if you don't have a pillow or mattress cover designed to reduce allergens. Or having lots of stuffed animals can cause issues with dust if sleeping with them. The sleeping flair ups could also be related to post nasal drip if he has other allergies since he would likely drain down the back of his throat when he went to sleep.
I have one kid with food allergies and the reaction that prompted us to see a doctor was wheezing and coughing that occurred 3 hours after ingesting the food. It also turns out he has asthma that is primarily triggered with illness. But having him seen and treated has resulted in incredible gains in reducing his coughing when sick. Before we knew he had asthma, he would cough a lot at every cold and the cough would linger. Now, when he has a cold, he is hardly phased by it and really hasn't had any lingering coughs.
It's definitely worth seeing a pediatric allergist and at least finding out if allergies is an issue. I recommend calling up your pediatrician and asking for a referral to a pediatric allergist if you cannot find one otherwise.