How to recover from a big mistake during your public organ performance?
Always treat your performance like improvisation. Never let yourself be restricted by the notes on the score.
When you make a big mistake, try to do one of the two things:
1. Go to the nearest half step up or down. That's all it takes to find a suitable note.
2. Repeat the mistake several times with some variations and use it as a turning point in your composition. This way it becomes intentional and part of the performance.
If you play from the score and play the wrong chord or note, see if you can keep the steady pulse and don't stop the flow. Instead think of the key this episode is in, and play a simple chord progression (a cadence) in that key which will give you time to adjust to where you are in the score and continue your performance.
Most importantly, breath to avoid panic and remember that your audience doesn't usually know each note of the piece (unless it's a popular hymn or anthem). Even then, rhythm is more important than melody.
Keep up the flow.