If it's an Aveirah to hurt a fellow Jew's feelings, is it likewise an Aveirah to hurt your own feelings? (e.g. via self-deprecation?)
I think we can answer this question with another question :)
Can one say lashon hara about oneself? See here and here for opinions on this matter. So whoever’s opinion you follow regarding this issue I believe it would determine if Onaat Devarim applies to oneself, and likewise would determine if it's an aveirah. Just to add that one of the points mentioned by Rav Aryeh Lebowitz was that the Chafetz Chaim implies in two places in his sefer Chaftez Chaim (1:9, 7:6) that there is no lashon hara on oneself. (I bring this up because there is no stronger proof then bringing the answer from the Chafetz Chaim himself, and likewise it wouldn't be an aveirah).