This article is from the Fleas, Ticks, and Your Pet FAQ, by tittle@zmall.com (Cindy Tittle Moore) with numerous contributions by others.
If you have left the head of the tick in your pet's skin, chances are
there will be an infection or an abscess in a week or so. Try
disinfecting the area thoroughly with 70% alcohol (it takes about 5
minutes for alcohol to sterilize an area). Ethyl alcohol is less toxic
than rubbing alcohol; vodka or any high-proof liquor will work, but
good commercial antiseptic cleansers are recommended. Then apply a
combination antibiotic ointment. If an infection occurs anyway, take
your pet in to the vet to have it drained.
 
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