According to the Rutgers catalog, NJ used to have contractual arrangements with several out-of-state vet schools, but the funding was eliminated in 2010. So as an NJ resident, you will be handicapped in vet school admissions everywhere (except at private universities, like Tufts or Penn, but they are especially competitive). You will probably also have to pay high out-of-state vet school tuition everywhere (again, except at private universities, but they charge high tuition to everyone).
You might check to see if it is possible to attend one of these out-of-state schools and qualify for state residency. If, for example, you studied at Auburn and were able to qualify as an Alabama resident, you would be in a much stronger position to be admitted to Auburn vet school than as an NJ resident, and you would also pay much lower in-state tuition.
I don’t know how feasible this is, though. In some states (like California), it is virtually impossible for out-of-staters to qualify as residents for tuition purposes, but in other states it is easier.