Those are three most common food triggers, doesn't mean they are your child's triggers. Also migraine tends to be a threshold thing. Your son may have a low threshold for migraine so small things are pushing him into migraine such as strobing sun, overhead flickering lights, dehydration (important with migraine to keep really well hydrated) , eating a food "trigger". It can be multifactorial. and vary day to day. So very frustrating.
I would keep a migraine diary to see if you can identify if he has migraines at a particular time and if there is some "trigger" .such as food, weather, lighting , hunger etc Some children get them at the end of or just after school as they are a bit dehydrated or hungry if they didn't eat much lunch as they wanted to get out to play. Some children have them at the weekend after a lie in. It is important to be very regular in habits and practice "sleep hygiene". Has your son's classroom got a dodgy strip light? or he is under undue stress of some kind or having a big growth spurt?
I take pizotifen it's one of the mildest migraine drugs in terms of potential side effects. It can make you a bit drowsy until you get used to it (a week or so) and is an apetite stimulant. It also takes awhile to see results as it needs to build up in your system. Start wth the lowest dose possible and add a tablet each week. I didn't get on with it first time round as the dose was too large but second time on the advice of a neuro built up slowly to the therapeutic dose.
www.gosh.nhs.uk/conditions-and-treatments/general-medical-conditions/headache
I would also consider having your DC's eyes tested as sometimes eye sight issues can cause headche and also getting a paediatric neurology referral as they tend to have more experience diagnosing and properly treating migraine than many GP's and can rule out any scarier diagnoses
and often recommend blood tests to show up if anything else is happening.
My son had low Vitamin D after covering up all summer due to acne medication and that had really sapped his energy and he was getting headaches on top when he started a new college as he was so tired and stressed by everything. The sun and strobing light really started bothering him too. The neuro picked up on blood tests for the vitamin D and prescribed a short course of a high dose and some lowest strength amitriptyline to help (he's older than your son). My son is so much improved.