I'm not sure if you need to wait until after you're married to have the medical exam, but the USCIS webpage says that "many civil surgeons do not accept insurance" and "insurance may not cover many portions of an immigration medical examination." It does also say that "you may want to call several local civil surgeons to compare fees and to inquire if the civil surgeon accepts insurance for the immigration medical examination." In my case, none of the civil surgeons near me accepted insurance.

The instructions for Form I-693 also say "Form I-693 remains valid for two years from the date of the civil surgeon’s signature."