Hi I'm a 13 year old girl who loves animals and would like a job working with them. I'm almost 14 and I'm going to need a job that well understand I need to go to school as much as I can.

You might be able to work with local groomers and do things like washing animals and sweeping. Or if you have neighbors that are busy then you could walk their animal for them at a fee.

Of course for any of this to happen you will need your parents permission as well as co-operation

A teen who wants a job has to apply to EVERY possible place in town. Shelters, pets shops, vets, groomers, kennels.
But saying that they have to understand that you 'need to go to school as much as you can' really isn't the way to approach this. First of all, they know you are in school. Present them with your available hours on paper. If you change them constantly you won't last long - a job is a job, and you can't just work when you feel like it or don't have to study for a test or stay after school.
About the only animal care job where they might be flexible is cleaning out cages and stalls because not many people want to do that.

Horse Stables.