Is the blinking voluntary (meaning he can stop it at will) or involuntary (cannot stop at will)?
Did the pediatrician note any eye discharge or redness to the eyeball or inner eyelids?
Does your son have a history of nasal allergies, skin eczema, or asthma?
Have you tried non-medicated artificial tears solution?
Can he tell you why is he watching TV out of the corner of his eyes? (e.g., trouble seeing)
We ask him if it is blurry and he says no, it is not. When we ask why he does it he says it helps him not to blink and makes them not so sticky.
The ped checked his vision at the office last week when he was there and the said it was 20/25. he always says that it is clear and never fuzzy or blurry.
With a lack of eye or lid redness/discharge, this points away from eye infection.
Excess eye blinking is possible with vision problems, but his vision screen tends to point away from this concern.
Visine would usually provide some relief if this were due to xerophthalmia (dry eyes), so this diagnosis is less likely.
With a history of eczema and seasonal (nasal?) allergies, this could be a case of mild eye allergies (e.g., to dust, pollen, mold). Some of my patients with seasonal eye allergy (allergic conjunctivitis) report dryness or stickiness first, then itch, redness, and eye discharge second. You might consider stopping the Visine and trying over-the-counter Alaway solution (1 drop in each eye every 8-12 hours, maximum twice daily) for allergic conjunctivitis for 2 weeks to see if there is any improvement (if this helps, your doctor may help with prescription-strength allergy eyedrops).