Surprised you don’t get automatic admission with your father as a professor. My mom’s also a professor, but the university is open admission. 
I’d say you have decent odds. I would definitely try to bump up that SAT score just a bit, although your score isn’t bad.
A lot of students don’t get better scores after retaking tests because they get so nervous about making sure they do better that it actually hurts their score. (This happened to me.) Applying later will mean that colleges look at your senior year grades, which you should probably take into consideration.
Because BU is so competive and test scores are pretty important, I would personally wait. Your odds of getting in shouldn’t change THAT much. But more importantly, go with your gut. Neither is a bad idea.