Do I have to get three estimates?

No. This is a prevalent myth repeated so much that it is almost a part of American folklore. Since you can get the car fixed wherever you choose, just get one estimate from the body shop of your choice. Be leery of the "approved" or favored shops of any particular insurance company, as they may be beholden to the insurer and not looking out for your best interests. When in doubt, a car accident attorney can help ensure you're not being taken advantage of and that your rights are protected throughout the claims process.