Like any other state laws, those of South Carolina were designed to put men in the militia. The Confederate government passed military laws designed to put men in the Confederate army. Physicians were needed at home as much as they were in the army, so enlistment for most physicians was voluntary. Physicians who had been in practice at least five years were exempt by the law of Oct. 11, 1862. Here's the law the clause reads --
XI. All physicians who now are, and have been for the last five years, in the actual practice of their profession; and in each apothecary store now established and doing business, one practical apothecary in good standing as such.
By Feb. 16, 1864, the exemption clause for physicians was strengthened to exclude only those who had been in actual practice for seven years and were at least thirty years of age.
Just a suggestion, but if you check South Carolina militia laws, they should include similar exemptions from militia service for practicing physicians. If the Confederate army did not need them, South Carolina could have required militia service of such men. Bear in mind that state laws always limited the period of time that militiamen were required to serve.