Volunteering to start is great. It will get you some experience, which many places require.
One bad thing about animal related careers is that they don't pay much, so if that's a factor, you might want to stick with a good paying job and just volunteer.
If that's not a problem for you, a good starting job is as a kennel tech or kennel staff for a vet clinic or kennel. You don't need a degree for that, and most places hire teens so I'm sure you could handle it.
Another option, if you have good office skills, is as a receptionist for a vet clinic, clinic, doggie day care, etc.
Most vet clinics hire techs as their staff, which does require a degree (usually). But some will hire vet assistants, in which no degree is required. You will have to decide if you are able to handle working at a vet clinic as you will see some horrific things come thru the door and deal with very ignorant and rude people......an
d sometimes even vets (which is why I am no longer working at a vet clinic currently)
I am currently a dog walker/pet sitter. I love the job. I get to pick my own hours, I'm outside for alot of the day, and I can pick and choose who I want to deal with. Of course, you won't really make any money for at least the first year of your business unless you maybe do alot of advertising. I don't advertise, and after a year, I am just starting to make money. Of course we are moving out of state in May, so I will have to start all over again (if I even decide to stick with it........not sure if I want to be outside in harsh winters).
Hmmmm......not sure what else is out there. Groomers usually need experience. If you like horses, you might be able to get work mucking out stables, there's alot of them in the Del Mar area. Just keep an eye out. And alot of places don't advertise in the paper, so if you're interested in working at a certain place, call to see if you can drop off a resume or talk to someone about a job.
Good luck with the career change.