I ran my former husband's (human) ophthalmology practice for 15 years and did all triage and have noticed that our vet uses human drops for eye issues.
With humans, teary eyes without significant discharge indicates irritation, which is most often caused by dry eye. It can be caused in some breeds such a Boston Terriers because of prominent eyes which protrude. Many environmental conditions can cause dry eye in humans such as blowing air in the car, ceiling fans, heating, air conditioning, etc. Can you see if the pup's eyes close completely when sleeping? If not, that could explain dryness and tearing. You might try a lubricating drop with transient preservatives (Refresh, Optive, Genteal, Systane are all good brands) or totally unpreserved lubricating drops. Do not use any "get the red out" drops.
As a rule, seasonal allergies cause itching and I would expect to see a dog rubbing its eyes if it sensed a foreign body or itching from allergies. My favorite allergy drop (Patanol or Pataday) is now OTC and I think it is okay for dogs.
If you see gooey or colored discharge or significant crusting, I would suspect an infection.
And, I'm not a doctor!