I don't know much about the Feingold Program but I would encourage you to look into diet. My daughter, diagnosed with ODD and depression, has turned into a easy child on the gluten/casein free diet. When she cheats, she shows her difficult child side again. We changed her diet for health reasons but we could tell in a few days that it was impacting her behaviour.
She was never diagnosis'ed bipolar but her t-doctor and I thought that is what would happen. A p-doctor we consulted for a second opinion suggested it might be Intermittent Explosive Disorder. I believe, after seeing the results in my daughter, that some people diagnosis'ed with mood disorders have an underlying food allergy causing it. I don't know if that means they don't really have the mood disorder or if they really do but it can be controlled by diet. Either way, it is impossible to completely avoid the foods so the problems will still be there at times. In my daughter's (and my) case, the medications helped for a while but kept needing to be increased. Removing our trigger foods has meant I have been able to get off my a/d, and my daughter has decreased her dose by 1/2. She cheats and/or makes enough mistakes that we haven't completely discontinued hers, but we are still working on it.
My other daughter was not diagnosis'ed with ADHD but was considered "impulsive, hyperactive, and easily distracted with attention issues" by the neuropsychologist. That has gone away now that she has eliminated gluten and casein from her diet.
My older daughter started the girlfriend/CF diet when she was 10. I am very indulgent with junk food as long as it is girlfriend/CF so she doesn't feel deprived. She is extremely compliant especially for an ODD child! I think the Feingold diet is more restrictive so I don't know what "junk" or kid food is available.
Instead of testing for allergies, you could completely remove the suspected food for a while and then re-introduce to see if you notice any changes. The top 8 allergens are wheat(I would eliminate all gluten, not just wheat), milk, soy, eggs, fish, shellfish, peanuts, tree nuts.
