Gentler nose blowing, rather than seeing a doctor, is the solution to this problem. Here's why.
Tears are made in the lacrimal duct. Tears flow across the eye to lubricate it and then drain through two holes called puncta. One puncta is on the upper lid and one is on the lower lid.
These puncta are attached to ducts that drain the fluid into a sac inside the nose. This lacrimal sac drains into the nose. Problems can come up when air and fluid go in the opposite direction. The small size of the openings and gravity usually prevent this.
It is sometimes possible to reverse the flow with enough pressure in the nose to force air and mucous back through the lacrimal sac and ducts and into the eye.
But this is not a good idea. It can force infected mucous into the lacrimal duct and eye, spreading infection. Stick with the gentle nose blowing.