To me it sounds like you should wait and see what sort of financial offer you get from Rutgers before you decide what to do.
Rutgers is a very good university. Over the years I have met a number of Rutgers graduates, and they have all made the university look very good. Three of them I met when they and I were graduate students at Stanford. Others include a former boss, some former coworkers, and some people I know in another way. They have all made the point that you can do very well with a degree from Rutgers.
However, you should wait and see what sort of financial offer you get. Starting at community college and transferring (very likely to an in-state public university) is another reasonable option.
Also, life is not a race. Taking a year off and working and reapplying for next year is also an option.
You should keep in mind that with a bachelor’s degree in psychology or neuroscience some sort of graduate degree is common. As such it would be helpful if you can to minimize or avoid debt for your bachelor’s degree.
And as @timeagain1 has suggested, there are a lot of ways to do well in life. This will work out one way or another.