Sounds like you have measurements pretty close to Hindman's 16' double ender. Yours is a few inches shorter, a tad narrower, a tad taller (so less flare to the sides overall). Overall, sounds like a pretty similar boat.
16' on these boats refers to the length around the sheer rail (the length of the sheet of plywood you need to make the sides).
As far as Class I-II or III, I'd say it'll handle whatever the operator can handle.