Definately not you cannot give human medication to an animal without the say so of a vet.
It isn't used for that and you shouldn't give anything to your pet without consulting your vet. Our meds are the number one cause of poisoning and poisoning deaths in our pets, benadryl poisoning is very common. It also may not be good with anything else your pup is on. You may be able to just call, speak to your vet about it and pick up whatever your pup needs and will be best, not to mention the correct dosage. Hope your baby is feeling better soon.