(a) The Mayor, pursuant to subchapter I of Chapter 5 of Title 2 [§ 2-501 et seq.], shall issue rules to implement the provisions of this subchapter. (b) The Mayor may establish, by regulation, additional types of medication that a student may self-administer and other illnesses for which a student may self-administer medication other than those provided in this subchapter. (c) All existing rules and regulations promulgated pursuant to subchapter III of this chapter [§ 38-631 et seq.] [repealed], shall remain in effect until rules promulgated pursuant to this subchapter become effective.