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If sounds as if your dog has developed conjunctivitis, commonly known as pink eye. You can clean the pus off your dog's eye with a warm washcloth. You can also flush your dog's eye with sterile saline solution like contact lens wearer’s use. Your vet will have to be consulted in order to get some medicine for your dog. Frequently an antibiotic eye drop is given for this condition. Sometimes Terramycin Ophthalmic Ointment is used for these problems. This is available at some feed stores like tractor supply.
You can read more about canine conjunctivitis here.
Canine conjunctivitis is a common eye problem. It can happen by itself or indicate an underlying problem. Finding the underlying problem can prevent future bouts with conjunctivitis. Underlying conditions that can cause conjunctivitis is KCS (dry eye, insufficient tear production, upper respiratory diseases such as kennel cough. Usually with respiratory infections there will also be coughing, sneezing, nasal discharge, fever, lethargy and loss of appetite. Conjunctivitis can also be cause by a foreign object in the eye or chronic irritation from a development problem of the eyelid and lashes where the lashes rub constantly against the cornea. It is possible that the soap may have irritated the eye leading to the discharge. In the future, you will want to flush the eye with the sterile solution if soap gets in the dog's eyes.
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