You can definitely give your zakah to your sister who is poor and is facing financial hardship. We are only forbidden from giving our zakah to those who are our dependents; since your sister is not considered as one of your dependents, you are allowed to give her from your zakah.
In fact, helping your sister in her time of need is even better and more rewarding than giving it to others. The Prophet, peace be on him, said, “Giving charity to one’s poor relatives entails double rewards: reward for charity and reward for fostering blood relations.” (Reported by Ibn Khuzaymah, Bayhaqi, etc.)
So, never hesitate in helping your sister with your zakah contribution if that is the only help you are able to offer her. If, however, you are rich and can afford to give her from other than your zakah funds, then that would be even better. In this way, you can give your zakah to others and help your sister from your sadaaqat (extra charities).