The fear of losing keeps me from playing chess

I have come to the realization that I do not play as much chess as I would like because my fear of losing. I usually like to compete in other things, and I am not a bad or sore loser by any means.

But for some reason when it comes to chess I take things way too seriously. I think it's because it is such an intense head to head duel, and I feel stupid when my opponent bests me although that is irrational.

I really enjoy puzzles and playing daily games, but when it comes to shorter time controls like 5-10 minutes I get a bit scared sometimes, so I just avoid it.

Do you have similar experiences, and how did you overcome it?