I dont think you have blocked tear ducts, usually one side is worse than the other in that condition. This does not sound infectious or allergic in nature either. It seems you have an overproduction of tears when there is irritating conditions, such as being outside.
I think you have a condition called meibomitis and this is why your eyes are tearing. Lets talk about the eye a bit. You may or may not know, the tears that help lubricate the eye are made of 3 different components. One is the actual watery component made in the lacrimal gland under your brow. It is where the water is made and if you get something in your eye or your eye is irritated, this gland goes in to overdrive and causes tears to be produced excessively. Second, is the mucous component and rarely do patients have a deficiency of this (often there seems to be an abundance). Third is the oily component of the tears and this comes from the glands at the base of the lashes, called meibomian glands. Those glands are often the culprit in someone with your symptoms. If those glands drain poorly, often as a consequence of aging, sometimes associated with rosacea (cause of adult acne), the tears are unstable and the eyes irritated and can tear.
Unfortunately, unless the glands become more functional, the situation never gets better. So the best treatment for this situation is the faithful and consistent application of heat packs which help the oils get moving. We are not talking a warm washcloth, that gets cold quickly, rather a heat pack that applies constant heat for at least 3-5 minutes at a time. If this does not provide good relief, your doc may consider an antibiotic like doxicycline, tetracycline or minocycline for 6-8 weeks or longer. These help the glands drain better. Also, use lubricants rather than allergy drops a few times a day, Refresh Celluvisc is a wonderful one to try. This regimen will help you make more stable tears and reduce the surface irritation and help make your eyes feel better, and in time the symptons wil improve. Take care and let me know if there is any more questions or concerns.
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