We investigate a posteriori error analysis for hybridizable discontinuous Galerkin methods for convection diffusion equations. A residual-type error estimator without any postprocessing solutions is proposed, and we prove that the error estimator is robust with respect to the error measured by an easily calculated energy norm in the sense that the efficiency and reliability constants are independent of the diffusion coefficient. Then the result and the method, that have been obtained and used for convection diffusion equations, are applied to linear-quadratic distributed optimal control problems governed by convection diffusion equations. We use the variational discretization concept for the approximation of control, and an efficient and reliable error estimator is obtained for the error measured by an energy norm. Note that the estimator is also robust in the sense that the ratio of the upper and lower bounds is independent of the diffusion coefficient. Finally, several examples are provided to validate the performance of the obtained error estimators.