Sorry to have to tell you, your find is definitely a civlian-usage "Nautical Motif" button, not an actual Military navy button. The actual ones never have an iron/steel back, because the salty-air environment causes the back to get rusty quickly, which makes a mess on the sailor's uniform.
Secondary to that ID, there is no match-up for your button's SPECIFIC emblem in any of the collectors reference books on US Navy (or British Navy) buttons.
Sidenote:
There is a single known exception to the "no iron backs on actual Navy buttons" rule. It is a 14mm diameter civil war era US Navy button which was used on the leather strap of a Navy kepi hat. Being on leather, it didn't matter if the button's back got rusty. Also, it never had to be "un-buttoned."