Their ducts can get blocked like ours, or it might be that he has a bit of an infection, Is there any thicked yellow/greenish discharge or stickiness of the eye lids? usually thats an indication of infection. He could have even scratched it or gotten something in it. Is the whites of the eye red and inflammed too? If he is blinking and rubbing his face that can be a sign that there may be something in it or irritation.

You could try bathing it with cooled boiled water and the sort of cotton wool that the fibres and fluff dont come off. Just wipe gently from the inside of the eye near the nose to the outer corner of the eye, only use each piece one and discard it. I have been given chloraphemnicol drops in the past for mine from the vet and you can get them over the counter at the phamacy now I think Optrex does one, however, I believe the strength is more then the dog ones, and as he is such a small breed and a tiny pup too, it might not be safe. I would perhaps use it on a larger older dog. Maybe try bathing it and see how it goes, if there is no improvement or seems to bother him, then probably best to seek vets advice tbh.

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Thank you for replying. I'll keep an eye on it over the next few days. It doesn't appear to be bothering him though and there is nothing coming out of it.