Clogged tear ducts are not the only cause of excessive tearing, but it can't hurt to flush them and see if it helps. Mikey tends to get clogged tear ducts every few months and we just go to the ophthalmologist who can do it without anesthesia, even with such a little dog.
Other physical problems include eyelid problems like distichiasis or entropion, both common in Maltese and may be subtle so your regular vet won't see it.
If flushing the tears ducts and the end of teething don't help, a visit to a veterinary ophthalmologist to rule out another pathological cause would be a good idea. If none is found, then it is usually the structure of the face that prevents the eyes from draining well and you can treat cosmetically to keep the staining minimal.