Your dog's symptoms donot seem to be associated with the incident of the trap and the rat.
I am in the Bay Area too (Saratoga) I would suggest that you consult with Deborah S. Friedman, D.V.M., Veterinary Ophthalmology, of the Animal Eye Care, in Fremont, especially if you do not have a vet. It is important to have this eye lesion checked in order to receive an accurate diagnosis and treatment as deemed appropriate.
There are several considerations. Your dog could have Ectopic Cilia, which is an abnormal eyelash that grows through the conjunctiva and is usually very painful and almost always causes an ulcer. This may also be Distichiasis which is an abnormal position of eyelashes on a lid margin that result in irritation of the eye.
IWhat type of breed is this? In regard to your dogs fur, does he seem to be continually scratching and licking? Do you use Frontline or Advantix for flea control?
Is the skin simply red or do you see bites or sores? If you can provide me with more details, I will be better able to provide you with further assistance.
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I wasn't sure if you meant "hair" or "ear". Thanks for the clarification.
My suggestion would be to go to Petco or any other pet store and purchase some ear wash. Click here to learn how to use it. This may help with the itching. Before undertaking this task, I would smell his ear to determine if there is an unusual odor as this could be related to a yeast or bacterial infection.
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Also, if you dog continues to scratch and itch, please let me know. I can tell you about using Benadryl and also discuss what foods he is eating as he may have allergies, for example, to corn and wheat, etc.