My son has extremely swollen tonsils, no spots, no discoloration (no red or purple), no pain, just a cough. what could it be?

Obstructive tonsils?: How long have they been this swollen? Also how old is he, and we would want to know how it affects his breathing, eating, speech, and sleep (snoring), and again for how long? If it is all very recent and accompanied with a runny nose and cough, we could attribute it to viral. But most likely we are considering tonsil and likely adenoid hypertrophy, and based on above factors directs treatment.

See PCP: There are many causes for swollen tonsils, including bacterial, viral, allergic, and developmental, to name just a few. Please have your son examined by your primary care physician for diagnosis and determination of appropriate treatment.