Dear heatherdu87, As you have mentioned that your baby's eyes are neither red nor any discharge comes out, I doubt if it is an infection. More probably it could some form of allergy
of the lids or the swelling could be the result of some other systemic disease which needs to be thoroughly investigated. You may try local anti allergic eye drops and oral anti allergic medication but only after consulting your paediatrician. Alternatively you should also consider going for a second opinion
by a differrent ophthalmologist.