Hello dear,
I know u r concerned about your baby. Dilation is required to make sure that there is no alarming power in your baby's eyes.. usually every eye specialist does that whenever u approach them for any issues. This is a small procedure and does not harm the baby. Without dilation, correct power cannot be confirmed. Rest other causes of watering is allergy of eyes(seen after 2 years) and blocked tear duct.
Next Steps
follow up with doctor and talk in detail of all concerns. I'm sure she will understand .