I think that BU is worth an application and is likely for admissions, but it is not a safety. Whether it is worth the cost for you is a completely different question.
You need to figure this out. Given that you are considering premed as an option, you need to budget for a full 8 years of university. By the time that you get there, medical school is likely to be well over $100,000 per year and might be close to $500,000 in total for four years. You do not want to take on this much debt. You would be better off if you do not even take on half of this as debt. If you are serious about medical school, then you need to find out what your budget is and find an undergraduate school for your first four years of university that fits that budget, preferably with no debt at all for your bachelor’s degree and some money left in the bank.
Four years at BU or Brown, plus four years of medical school, might very well cost $900,000 by the time that you finish. You do not want to borrow half of this. Even borrowing 1/4 of this is quite a bit of debt even for a doctor.
Your chances of ever getting to medical school will most likely be almost exactly the same regardless of whether you attend Rutgers or BU or Brown for your bachelor’s degree, and Rutgers is a very good university. Brown might get a higher percentage of its incoming freshmen into medical school, but a lot of this (some might speculate possibly all of this) is due to the high average abilities of the freshmen who show up at Brown in the first place. Premed classes are going to be academically very demanding at any of these schools and will be full of very strong students, most of whom will never make it to medical school (although in some cases this will be because they just decide that they want to do something else).
You also should figure out how your GPA is calculated. However if you are third in your high school and assuming a class of at least 100 students, then you are doing well.
The large majority of students who start university thinking ‘premed’ end up doing something else. If your particular form of something else includes a bachelor’s degree in psychology, then some form of graduate school is very likely. If you save college money for medical school, and instead go for some other graduate degree, then the money that you saved can still be very useful. As one example master’s degrees are typically not funded, and while PhD’s usually are fully funded, the stipend is minimal and having some additional help from parents can make the whole marathon more tolerable.