Can I sue my landlord?

The terms of the written lease (if you have one) will control. She cannot evict you before the lease expires unless you have materially breached the agreement. If you do not have a written lease, then it is presumed a full period notice (30 days after the 1st of the month or whichever day rent becomes due each month) by the landlord is sufficient. If you do not move after that, she will need to file an unlawful detainer action and obtain a court order to have you removed from the property (the Sheriff will come forcibly remove you). But beware, if you make her jump through hoops, you could end up on the hook for the related expenses, including attorney fees.