Well, Watson admission is kind of weird but if I were you I would probably try to score as high as I can on the SAT the next time you take it. Especially the math part. Also, make sure your current grades stay where they are. So you do have a shot. Unfortunately, its really hard to transfer into Watson once you are already at Binghamton so I honestly wouldn’t suggest doing that.
So yeah, you have a chance but I would also apply to other schools (other suny schools with engineering programs, maybe a school like RIT). If you do get offered a spot at Harpur, I probably wouldn’t take unless you are fine with getting a liberal arts/science degree instead of an engineering one.