I read your post different than TTMinhT. I agree with TTMinhT if your therapy dog is for your physical disabilities. However, from the word "volunteer" in your post, I assume instead that the dog is used for the comfort of others.
If for the comfort of others, and if done under the auspices of a tax exempt hospital or other organization, then the direct out of pocket expenses would be deductible as an out of pocket charitable contribution, not as your own medical expenses. Whether medical and grooming expenses are a "direct" cost depends on any other use of the dog, such as for a family pet. If the time spend as a therapy dog is not material, then those expenses would be nondeductible personal expenses. Mileage to the hospital, tax-exempt assisted living facility, etc. would be deductible but at the medical rate.
