Animal as sensitive to energy, light, color, etc just like we are. Thus, depending on what it is you're trying to heal, you could look into color therapy, crystal healing ,etc. Animals have chakra's too and they can be healed emotionally, spiritually, etc just like any of us can. There are even acupuncturists that offer their services to animals. You could try looking to classes or courses on that, if you have the time and resources to do so.
If it's a serious injury or illness, you do need to take the animal to the vet, however.
I actually came across a few articles that you might be interested in as well. I've added the links below.