They didn't run the course for my child. He had severe blocked ducts in both eyes and it was miserable. Right before he turned a year old, I had the procedure done to get them unblocked. They drop numbing liquid in the eyes, then stick a curved needle through the tear duct. They have to strap the baby down and hold it's head tight.
If the child is over a year, they will have to anesthetize him, so that is why I chose to do it before it got to that point. The Dr. told me if I had waited, the ducts would not have cleared because it was very bad.
I did the prescribed ointment, the warm compresses, the massage, the breastmilk... nothing worked and my baby was so uncomfortable and stressed and it was so awful for him having his glued shut eyes degunked every day.
The procedure lasted but minutes, (though he screamed the whole time)... and his tears were a little bloody for a day or two, but it was so wonderful, he was so happy afterwards and we never had to hold him down to clean his eyes again.
I would highly recommend it, but since your baby is only 4 months old, I would continue the massage and compresses for several more months before you do the procedure.