Flying immediately after diving significantly increases your risk for DCS, particularly shortness of breath, and difficulty breathing brought on by the formation of pulmonary micro-emboli.
Over the last few decades the recommendations regarding the time to wait before flying after diving have changed many times, varying between a quite tolerant 12 hours, and a more conservative, but more exacting 24 hours.
The general consensus has come down to waiting 12 hours following a normal uneventful dive; waiting 24 hours after a dive considered more demanding than normal or following multiple days of consecutive diving; or waiting at least 48 hours after a dive that is considered extreme, or that was, for what ever reason, beyond recommended recreational diving limits.
Divers that use a dive computer should follow its no fly recommendations, and wait until it has cleared you for high-altitude travel or flying in an airplane before doing either.