I've had a swollen tonsil for about a year. It's not painful at all and doesn't affect breathing much. What can I take to make the swelling go down?

Consult an ENT dr. If you had this "swelling" for one year, most likely is not a "swelling" but an "enlargement" or hypertrophy. Please, consult with an ENT specialist. The treatment could be surgical (if it's really symptomatic).
See an ent. See an ENT doctor as it could be a tumor or something benign. Best to get it checked out asap.