This is a tough argument since Nora actually becomes independent in the end. Prior to that, she is Torvald's play thing, and her spending habits are funded by him. She also lives in his house and, as society intends during her time, she is her husband's property.
One could argue, however, that Nora maintained a senseor feeling of independence by falsely believing that she can be in control of Krogstad in the same manner that she takes control of her husband's illness by borrowing money. All those times in which she takes charge of a situation may be looked upon (by her only) as signs of independence. However, all that is fantasy: She is bound to Krogstad by way of her debt, and she is bound to Torvald financially and socially.
When she finally tells him the truth in the end, she also decides to abandon him despite of the fact that she is bound to him in so many ways. This is her true and honest independence: When she literally gets rid of him and goes about her business for the first time ever.