Rats! Okay, how about this? Could you offer to volunteer at the vets office (or another vet) for a week or so to get your foot in the door? Tell them that you'll volunteer your time for a week or so and ask them to evaluate your performance and consider you for a paying job?

I did something like that in 1990. I volunteered for 2 weeks (I think) and it led to a great job and I learned so much.