Bel-B,
I worked with a lad many years ago who had tear duct problems, his handkerchief would be soaking wet with wiping the tears away and his eyes were permanently red. Although I left that employment I happened to bump into a ex-work colleague and asked after this lad's health, apparently he went on to have a operation to repair his ducts and the problem ceased. Like most operations, I would imagine they will only resort to surgery in the most urgent cases as there are risks involved as in any kind of surgery. Hope things improve soon and it isn't to distressing for you!
Nigel