Is performing two rak'ahs of prayer as a way of thanking Allah after 'Isha' for the mother's recovery, fulfilling a vow made to oneself, an innovation (bid'ah) or a mistake?

If the questioner intended to pray two supererogatory rak'ahs after 'Isha' as a thankfulness to Allah if his mother is cured, then this is considered a vow of justification (nadhr tabarrur) that must be fulfilled, and it is not considered an innovation in religion. However, if he did not intend it as a vow, then nothing is binding upon him.