No, you didn’t give her an eviction notice. Only a judge can order an eviction.
You gave her a “Notice of Termination of At-Will Tenancy” (exact title varies by state). That was her official notice that her month-to-month tenancy has been terminated.
Assuming you followed your state’s laws to-the-letter on serving her that notice (laws vary WIDELY by state as to who can serve the notice, when, etc), your next step is probably to have her served with an “Unlawful Detainer” notice. In my state, that’s the step just before an actual eviction.
Follow your state’s laws TO-THE-LETTER on having that notice served. If you screw it up, you have to start all over with a new 30-day notice.
If she still won’t leave after receiving her Unlawful Detainer, file for an eviction. It will be granted, since you’ve legally terminated her tenancy.
Then you pay the fee to have law enforcement officers remove her from your home by any means necessary, and in my state, you will be required to change the locks while they’re onsite. They will trespass her off the property, which means she can be arrested for ever setting foot there again without your EXPRESS permission.
