Usually blocked tear duct in infants, resolves on its own by around 1 year of age.
And the usually recommended treatment is a regular massage
If after regular massage too, the condition does not improve, then you will be referred to an Eye Specialist who will do minimally invasive procedures
like probe and irrigation- done as outpatient procedure.
Since you are very anxious, you may visit an Ophthalmologist and get his opinion too.
Hope my answer helps you.
Wish your daughter good health.