The schools in my state (Oregon) dont require a TEAS but they do require a 3.5 (prereqs only) for most BSN programs and there is no way that a B in anatomy/physiology is competitive even though you have really good grades besides that one. Also for most BSN programs in this area you get a lot of extra points on the application for 1000+ hour as a cna/ma/ems, and have a previous bachelors degree. If you are already in your third year maybe getting a bachelors degree but I am no sure what kind of system the schools you applied for use.
If I where you (which I was 2 years ago) I would retake any classes you have a B in, get more direct patient care experience, and I dont know anything about TEAS scores but if it is average or lower I would try and get an "above average" score, and possibly get a bachelors.
Whatever you do DONT GIVE UP! Youll get it, it only took me 6 years to get in