Would using my medications more frequently than prescribed speed up the clearing of my acne?

Acne use meds often: You doctor has prescribed medications for you (i assume) to be given, used, applied at specific times. More does not make it better. More pills would be dangerous; more frequent applications of the topical medication might cause burning and peeling. Stick to your "doctor's orders.".

Nope: Using them as prescribed will rid you of acne the fastest and most safely.