I'd suggest trying games where failure is a goal-post. I had similar but less severe issues where I hated hardcore difficulty in games because I would never finish them.
Oddly enough roguelike games broke me out of that. I'm usually a very safe kind of player, I prefer to turtle it up, take my time, and proceed carefully.
Try something like Rogue Legacy, yes you will die, a lot, but each time you die you get BETTER. You get to buy new upgrades for your character and try new character types and find your favorite.
Roguelike games are specifically designed with dying a lot in mind, and while it may seem counter-intuitive to go with a game that intends to kill you over and over, it's sort of like facing your fear head on. Roguelikes quickly teach you that death can be a fun part of the game, and while at times it may be frustrating, it's more of a "I'm going to beat this" kind of feeling instead of a hopeless throw your controller on the ground kind of thing.
Spelunky is another good one to try, it's got a very easy control scheme, but the levels are challenging and quick to complete and you learn a lot each time you play.
Don't Starve is pretty unforgiving in it's difficulty however each time you die you gain experience based off how long you survived which can unlock new characters to play as, which gives dying a sort of reward.
Look for games that have the following:
-Rewards for death, where even dying gives you something new to help you.
-Shorter Playtimes, the game doesn't have to be short but something where dying doesn't usually mean losing hours upon hours of work.
-Multiple playstyles either through different classes, characters, skill sets, etc. that let you try different approaches each time you start over.
Yes you will die, but dying isn't failure, it's learning to succeed.