We develop a conceptually simple scheme based on a master-equation approach to evaluate the full-counting statistics (FCS) of elastic and inelastic off-resonant tunneling (cotunneling) in quantum dots (QDs) and molecules. We demonstrate the method by showing that it reproduces known results for the FCS and shot noise in the cotunneling regime. For a QD with an excited state, we obtain an analytic expression for the cumulant generating function (CGF) taking into account elastic and inelastic cotunneling. From the CGF we find that the shot noise above the inelastic threshold in the cotunneling regime is inherently super-Poissonian when external relaxation is weak. Furthermore, a complete picture of the shot noise across the different transport regimes is given. In the case where the excited state is a blocking state, strongly enhanced shot noise is predicted both in the resonant and cotunneling regimes.