I'm glad you asked your doctor, because if there was something to be concerned about, that would be the best place to start.
I'm wondering of your baby just recently "discovered" his eyes. Sometimes when babies suddenly become aware of a part of their body or a noise they can make or a movement they can control, they like to practice it and play around with it. My parents have a picture of me in my crib the day I "discovered my toes." Maybe your son recently became aware of the fact that he can control the blinking of his eyes and they don't both have to blink at the same time.
If your doctor says there is nothing to be concerned about, that is most likely the case. It can't hurt to write things down and keep track of any changes. But it is important for you to try to relax and enjoy your son.