@kokopta
Whether you are applying for direct entry BS/MD or regular UG, you need to apply coming fall. Submission dates may be early for BS/MD. But you should take your SAT and/or ACT this summer, preferably before school starts.
Not many schools will offer Neuroscience major. But you can do any major and still do many courses related to Neuroscience. Major is typically 35 to 50 credits only in any school. But you can take whatever courses you like to focus.