Within the Schwinger-boson approach for the t-J model, the single hole problem in a two-dimensional quantum antiferromagnet is studied by using the quantum Bogoliubov-de Gennes formalism which treats the distortion of the spin background and quantum spin fluctuations on an equal footing. Several self-trapped localized hole states are found in the distorted spin-background as in the case of an anisotropic Heisenberg model. These localized hole states survive at finite temperatures when the antiferromagnetic order becomes short-ranged. The energy separation between the two lowest states is reduced by considering the spin-background distortion, but it remains finite. (author). 17 refs, 5 figs, 1 tab.