A couple of points. First, a practicing physician could not be conscripted. Civilian physicians sometimes chose to serve the military as contract surgeons on a temporary basis, but that was an individual choice.
On the other hand, anyone who joins the military looses his freedom of choice. The Medical Director's office in Richmond determined where a surgeon or assistant surgeon served. As a matter of expediency, initial nominations for regimental staff positions were normally honored. However, once regiments entered field service and vacancies arose due to resignations or hospitals needs for experienced staff, the MDO transferred surgeon and assistant surgeons to meet needs. Preference for medical officers from the same state as the offices and men held as often as not, but not more so.