not sure where my original comment went but anyhow...Looks like the makings of a cottonwood tree. We have a huge one in our yard and while it provides tons of shade and rustling, it is exceptionally dirty and litters "snow" in the yard and gets stuck to the window screens and the air conditioning units.
Our neighbors cottonwood tree creates snow drifts too. I hate the darn thing, but love the birds that live in it. Even had a great horned owl who took up residence there for a while.
Late to the party - but these are the SEEDS and do not contain pollen so you can't possibly be having an allergic reaction to them (unless you're eating them or rolling in them and then I'd suspect a different reaction than itchy eyes.