We had this same thing happen during my daughter's kindergarten checkup this summer. I pushed to get a referral to a pediatric ophthalmologist, and I'm glad I did. The specialist went through a whole series of tests with her, and discovered that she has an astigmatism. (Basically one of her eyes is being pulled into a football shape by the surrounding muscles, instead of the normal basketball shape.) They said that if it is caught and corrected with glasses at this age, when a child is first learning to read, their eye/brain development will be totally normal. If you wait, the brain will learn to "re-route" information through the good eye only. I know this to be true, because nobody caught my astigmatism until I was in junior high, and I actually cannot read with my left eye. I can see the letters, they just don't make any sense to me. (I know, weird.)
So with my daughter, they prescribed glasses, which she now wears when she reads or does any kind of classroom work. She loves to wear them (maybe the fact that they are Disney Princess glasses has something to do with it, LOL). I was afraid other kids would make fun of her, but they don't.
I would just really recommend that you push for a referral to an ophthalmologist sooner rather than later. Why chance having his eye-brain development not happen correctly because the pedi said the problem may or may not work itself out? Get your son assessed by someone who can figure out what the problem is (if there is one) and correct it. It will benefit his long-term development, and they try to make the visit as fun for kids as they can. My daughter loved her eye doctor and now says that's what she wants to do when she grows up - so it was a positive experience for her!