You can claim
expenses related to your pet only if it is a guide dog or other service animal in Medical expenses.
On the subject, IRS Publication 502 - Medical Expenses says:
"You can include in medical expenses the costs
of buying, training, and maintaining a guide dog or other service animal to
assist a visually impaired or hearing disabled person, or a person with other
physical disabilities. In general, this includes any costs, such as food,
grooming, and veterinary care, incurred in maintaining the health and vitality
of the service animal so that it may perform its duties"
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