Yes, as they charged to care for your pet the cost of dealing with any injuries is recoverable. I would suggest, after having a complete report from another vet, and fully documenting the injuries you consult with an attorney.
You may have a case if the veterinary clinic breached its duty to provide a reasonable level of care for your dog. You would have the burden of proving, inter alia, that your dog's health problems occurred as a result of an unreasonable level of care exercised by the veterinary clinic. I would consult an attorney licensed to practice law in Florida with animal law experience.
Can you prove the dog had no injuries prior to being boarded? Did you immediately take the dog back into the vet’s office and ask about the wounds? Did you take pictures of the wounds? Did you take the dog to another vet for examination within 24 hours? Do you have a vet that will testify on your behalf?
While veterinary malpractice is a valid cause of action, such suits are very expensive to litigate. It basically becomes a battle of the experts. In addition, the damages awarded are generally not very high unless what the vet did was truly shocking and outrageous - basically, if you win, you might get reimbursed for any medical care.
Short of litigation, you can file a complaint with the American Veterinary Medical Association, http://www.avma.org/
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.