My 3 1/2 mo old has a blocked tear duct. It's worse some days, better others. For those worse days, what signs mean he might need to see the doctor?

Wait. At 3 1/2 months there is still a chance that the blocked tear duct will resolve spontaneously. Try massaging near the inner corner of your child's eye. If, by 6 months, the tearing has not improved it is time to see a doc.
Blocked tear duct. You need to be performing the crigler massage and warm wash cloths to remove crusting and keep eye clean. If the eyelids swell, the eye gets very red, or it is causing pain, you need to see an eye doctor.
Dacrocystitis. Lacrimal duct stenosis is a benign condition and very common. Simply, the tear duct hole is not big enough to drain well yet. On occasion, this blockage goes beyond the usual tearing and scant discharge to develop into an inflamed, swollen and tender duct with redness overlying the area. This is dacrocystitis and requires a doctor's visit.