I have blepharitis which sounds very much like your problem.
No one has suggested blocked tear ducts, so maybe not the same.
Bathing eyes twice a day helps, with a little baby shampoo in water when really sore, does help. I have drops on prescription in a little capsule which are better than those optician sold me.
I wear swimming goggles in shower to keep out perfumed hair products. I can't wear eye makeup or use eye cream, and even face cream seems to creep up my eye wrinkles!
Big hat when sun out as well as sunglasses. I haven't solved the wind problem though, and just stream and stream.
I never got to see my GP, just practice nurse who said she gets watery eyes sometimes, so that's ok then.
I did manage to chat with nurse in eye clinic when I was working at the hospital, who said I was doing all the right things.
You do need to get to your surgery though to get checked out.