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With a 9 year old chihuahua, the first thing I would suspect with a swelling near the eye and her not wanting to eat would be the possibility of a dental issue. An abscessed tooth will cause swelling under the eye which can cause the eye to be puffy. Of course she would not want to eat with a painful tooth either. So the first thing you will want to do is check for any dental issue. Look for red, inflamed gums, tarter buildup, broken or obviously decayed teeth especially in the back of the mouth. You will need to have her seen if you find any dental issues so they can be resolved and antibiotics given.
If this does not seem to be a tooth issue, it may be the start of an eye infection such as conjunctivitis or she may have even gotten a foreign object in the eye causing her discomfort. You might try flushing 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. 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. Here are some common Eye conditions.
Allergies can cause localized swelling as well. Insect bites are common causes. Benadryl can be given at a dosage of 1-2mg per pound every 8 hours. An allergic reaction might also cause some swelling in other areas or some nausea. Given Corina's age and not wanting to eat, I'd try to get her seen as soon as you can. To help prevent hypoglycemia (low blood sugar) from not eating rub a little karo syrup or pancake syrup on her gums.
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