You should show him to his pediatrician and if he finds out that he needs to see a pediatric ophthalmologist he will reger you. Good luck
If your child is truly experiencing excessive blinking, bring him in for an examination by your pediatrician. Excessive blinking can be caused by problems with the eyelids, front part of the eye, occasional exotropia (turning out of the eye), stress, or any other discomfort. Older children may blink excessively if they need glasses (refractive error, attempt to see more clearly), or as a tic manifestation. While tics can happen in infants, it is extremely rare. Isolated blinking tics tend to be transient, resolve in a few weeks, and do not signify an underlying neurological problem. No brain imaging needs to be done. Children with multiple tics (other movements and/or vocalizations) should see a pediatric neurologist for further evaluation.
Your pediatrician can examine your baby's eye to see if the conjunctiva (membrane covering eyeball) might be irritated and pink or red, and if so, ascertain the cause of the irritation. Your pediatrician may also refer your baby to see an ophthalmologist to look for other causes in the eye.