Can I be a Neuroscience major AND not dissect any animals?

That's a tricky one. あなた may find it depends on the college. You're still a junior so you've got time to do some research; I suggest あなた try looking up (or even contacting) the colleges あなた are interested in and asking them about your situation. Make sure あなた end on a positive note によって suggesting an alternate solution that you'd be happy to do.

To be perfectly honest, I don't have my hopes up about this, as from what I understand dissection is quite a big part of neuroscience and the high school alternatives are probably not acceptable at college level. But あなた never know until あなた try.

Who knows? あなた might inspire them to come up with an alternative if they don't already have one. It's worth a shot. Good luck!