I'm not sure if they would shrink, depends if they are normal size now.
Have you considered taking him to see a naturopath or nutritional therapist? Maybe someone who can test for
food sensitivity issues.
Avoiding all refined foods like sugar, white flour products, hydrogenated fats/margarine, cookies, etc helps a lot. If you have a juicer, make him some fresh vege juices and also have him eat plenty of fruit.
Basically, mucus forming foods need to be cut out - dairy is for certain, for others it may be wheat/gluten, eggs, nuts etc. they're common ones.
You can find powdered Vit C (ascorbic acid), also there is a product called Emergen-C available from many websites (and stores in the US) also check iherb.com who sell it. Kids like it and it provides good Vit C in a fizzy (sugar free) form.
Also, since the tonsils/lymph are connected to the immune system, you might want to investigate getting some herbal remedies like echinacea, olive leaf, oil of oregano, pau d'arco in tincture form.
Also, these teas are useful, you could make them up and let them cool down, add a little honey, mollasses, stevia or maple syrup to sweeten: nettle, dandelion, Echinacea, yellow dock, goldenseal.
Also, sweating cleanses the lymphs. Give him a bath with a large cupful of
Epsom Salts every night, let him bathe for 20-30 minutes.
The lymphs sometimes back up because the colon is blocked (poor food choices may be a reason). Is he having regular bowel movements? If not, he needs more fibre in his diet. Also, you can consider some oxygen based cleasers like colosan/homozone/
Oxypowder to remove some old waste.