Swimmer's Ear is the layman's term often applied for Otitis Externa; an outer ear infection. The medications you've be prescribed are acting on the malady in three ways:
Hydrocodone is to offer some pain control and act as an antipyretic (fever control, if you have one).
Neomycin is a combination antibiotic/antiinflammatory suspension. It will help treat the causitive organism and decrease the inflammation in the area.
The Amoxicillin is another antibiotic to attack the causitive bug.
The timeliness with which your hearing will return depends directly on the severity of infection and inflammation you have. The less of both, the quicker the return to normal. The inverse is also true.
Be careful with your use of cutips in the future. Many swimmer's ear cases in adults are caused by aggresive ear cleaning...not to mention swimming in the Anacostia River