No. The U.S. Citizenship and Immigration Service maintains a list of approved doctors. These doctors are referred to as civil surgeons and you must go to one of these approved doctors for your medical exam and vaccinations. The medical exam typically runs between $150-$300.
In the St. Louis area, there are approximately 8 facilities that offer the immigration medical exams. You may access the names and contact information for local civil surgeons by clicking here.
The civil surgeon will have the forms that need to be filled out and will give you the forms in a sealed envelope. The primary form used by the civil surgeon is form I-693. Do not open the envelope as that will void the results and you will have to get another sealed envelope.
Please keep in mind that you must also provide documents to USCIS that show you have been vaccinated against many types of diseases. You should bring your vaccination record with you to the exam. If you have not had a particular vaccination, you will receive it from the civil surgeon.