Hey girl! Not to worry. 14.3 is a common height for barrel horses, the most common range right around 15hh. Your height is not nearly as much of a concern as weight and balance. I am 5'9 also and have had great successes on both my 14.3hh gelding and 15.2hh mare concerning barrels. Another thing I would be concerned about is my horse's ability and conformation for the sport. Although Barrel racing is not a long, drawn-out event, it does put alot of stress on a horse's bones, legs, hooves, joints. Good conformation fit for barrels is a plus. Good luck and have fun