In most cases you can't just elect to be an independent contractor or not. There's no such thing as an independent contractor EMPLOYEE. You are either an employee or a contractor. I would suspect that the nature of your work mandates that you are an employee NOT an independent contractor. This decision is NOT made based on whether the employer withheld taxes or not, it's the other way around, they are required to withhold taxes from employees and they are not for contractors. If you are an employee it is not your responsibility to tell them that taxes need to be withheld. They are REQUIRED to do so. In fact, it is on you to tell them NOT to withhold if you are in one of the very few situations where you are exempt from paying tax.
You should get "her" to give you an explanation of the money paid and withheld. They are required at the end of the year to provide you a W-2 if you were an employee or a 1099 if you are a contractor (and made more than a small threshhold from them). If they erroneously failed to withhold taxes from you earlier, they indeed can take it out of a later check. Again, I would demand an explanation.
If they are indeed classifying you as a contractor, you can indeed challenge that. I suspect at this point you are exempt from FICA so it probably won't make too much difference. Once you get resident work authroization, you may wish to watch such distinctions more carefully.

