Skin spots and tearing are very common in several breeds, especially in Poodles.
The causes are diverse and range from clogging the naso-lacrimal duct to out-of-place cilia. Some rations can help when these symptoms are caused by acidity of the tear, and some professionals recommend medications for the treatment. The success of the treatment will depend exclusively on the correct diagnosis of the cause, so you should always look for a trusted veterinarian (check a complete list of professionals who can help you).
Today, with the great dismemberment of veterinary specialties, it is frequent to find professionals specialized in veterinary ophthalmology. A professional in this area will be able, in addition to the diagnosis, to determine the treatment - which, in some cases, can even be surgical.
Hope this helps,