How should medical mileage be recorded? Do I need beginning and ending mileage for the year like for a business if I'm not using the vehicle for a business?

All medical stuff, including mileage is dealt with under the Deductions and Credits tab in the Medical section. Under the "Medical" heading is a section titled 'MEdical Expenses". You work that through and you will be asked for medical miles driven on one of the screens. You'll see that total miles driven for the year have nothing to do with miles driven for medical need.