Core strength aids balance, as you probably are aware. I don't believe your height is an issue, either. And the advice about the high heels is right on target.
But I also don't know how strong you are. I have danced with women whose arm strength is so weak that their arms crumple on certain moves. It usually meant they were not very strong in the core area either and their dancing was a bit "wild" and disorganized because of it.
My wife often tells me that if I improved my core strength, a lot of the more difficult moves we try to do would be a lot easier. I tend to lose a little balance on occasion because at age 55 my midsection is much softer than it was 30 years ago.
But give that some consideration. Yoga, strength exercises and anything that works the core is a positive for a dancer and real plus for overall balance.