Both of my older children, now 5 and almost 7, had this condition (dacryostenosis) to the point of requiring surgery for probing the duct and having a stent/indwelling tube placed. As the literature states, if the condition does not spontaneously resolve with massage by the time a child reaches 12 months of age then surgery is required. When you compare the risks vs. the benefits, in my mind, there was NO question!---The surgery needed to be performed.
My oldest's procedure was not without difficulty. The anesthesia was not a problem but his canal was so scarred they almost recovered him so that he could have more extensive surgery with an otolaryngologist(ENT) AND an ophthomologist to reconstruct his tear duct when he was older and the structures were larger. Post-op required follow-ups to determine if the stent was still in place as some kids rub their eyes and pull the stent out----not a problem as long as the duct stays open. But if the goopy eye discharge recurs, then your child will likely need surgery again. My son had the opposite problem---the canal was so scarred that the stent, usually removed in the doctors office during a 6 month post-op follow up, needed to be removed under general anesthesia--AGAIN! But again, there were abolutely no problems with the anesthesia.
My next experience with my now 5 year old was similar in that her duct did not open into the nasal canal. Her procedure, again at 12 months of age, was not described as needing to recover her and perform a second surgery with the ENT, like my son, but the time under anesthesia was extended to re-create her duct with the probe. Her post-op was tougher because she came out with a bloody nose and seemed initially more uncomfortable than my son but her post-op was inevitably unremarkable. She, however, did not have the scarring problem and when she went in for her 6 month post-op the stent was gone without recurrence of clinical signs---she must have pulled it out.
My son's inital surgery was out of state but the subsequent surgeries were performed by the ophthomologists at Children's---The ophthomologist we had is no longer there but the experience was ideal. I don't know if Children's Eye Physicians does this too but I have recently become acquainted with them for one of my kid's near-sightedness and have been impressed with their pediatric bedside manner.
A simple walk through---It's an early morning out-patient procedure. The kid's are fasted the night before with clear liquids and water okay. Both the anesthesiologist and ophthomologist spoke to us at Childrens. They have a great play room and kids movies running while you wait. The kids each brought a comfort toy---The nurse took my son, and his stuffed kitty, back without a problem but I had to go with my daughter and hold and talk to her while she was induced. They use gas anesthesia with flavorings/scents like bubble gum or banana. My kids were induced with Sevoflurane and maintained on Isoflurane. We were at the hospital about 7am and I recall leaving no later than 2pm that day.
The one thing I do remember---The nurses in the recovery room both out of state and here in Colorado asked if my kids had the "sedative." It is offered pre-op, especially if you think your child will have a lot of anxiety away from you and the one they used at Childrens is midazolam---same family as valium. I DID NOT request it for my kids for these reasons: 1) As I stated before my son didn't need it, he'd go with anyone! AND 2) When they were recovering my son, the nurses said it was a good thing he didn't have it because it made recovery rough. Therefore, when they came to give my daughter her pre-anesthetics, I questioned what they were giving her and told the nurse I did not want the midazolam given. She went and found the anesthesiologist, because he had not spoken to me yet and we discussed my concerns. My daughter did not get the midazolam but it was also too late for her to get a pre-op dose of Tylenol. I was a little angry at first but as it turned out---As I described before, her probing was extensive and she ended up getting morphine because of all they had to do.
I think any time an MD recommends surgery and you are not comfortable with the recommendation---ALWAYS get a second opinion. KUDOS to you for having the courage to do that. Too many times I have seen friends or family members not question a doctor simply because they are a doctor. The fact that remains is that they are human, are capable of mistakes and no one but YOU is the best advocate for your health and your children's.
I apologize for the length----I just felt since I had been through this TWICE I could provide a greater perspective. FWIW--my other child was born with a blocked duct too but this spontaneously resolved with massage by 6 months of age. Hopefully for you, your daughter is the only one that has this but of all the conditions our babies can be born with, I would feel comfortable tackling this one anytime.
Best wishes---Feel free to contact me if any further questions.