Mouse only games

If you're okay with visual novels, most of them only really require clicking. I'd recommend like... Steins;Gate if you're interested in that at all. Not really a game but... it's interesting enough and simple enough to engage with in your current form.

Crusader Kings II

tower defense games, like plants vs zombies or defense grid.

Really surprised no one suggest Civilization

Mirando tu biblioteca, tengo algunas recomendaciones

• 9 Clues: The Secret of Serpent Creek / Dark Arcana: The Carnival / Mind Snares / etcetera - Cualquier juego del genero Objetos Ocultos de Artifex, todos son buenos, con la justa dosis de puzzles y una trama que suele enganchar.
• Clickr - Un "clicker" de puzzles que se basa en el clásico "Conecta 4". Parece simple, pero antes de darte cuenta ya te ha robado el día.
• Knights of Pen and Paper +1 - Un RPG divertidísimo, con muchísimas referencias y que engancha muy rápido. Te lo recomiendo completamente y no te doy spoilers.
• Pixel Puzzles Ultimate - Rompecabezas, así de simple.
• Puzzle Agent 1 y 2 - Buenos Point & Clicks con su peculiar dosis de puzzles y un humor bastante jocoso.
• Stronghold / Men of War / Company of Heroes - Estrategia pura, cualquiera de ellos es una excelente opción.
• Tea Party Simulator 2015™ - Puede que no sea el juego más divertido o el más pulido, pero si quieres un verdadero desafío basado en físicas, este cumple de excelente manera.

Sin más, ¡espero que mejores y te diviertas! (Y te he respondido en español puesto que no le veo sentido hacerlo en inglés ya que tu perfil indica que eres de Argentina).

Stardew valley is playable on mouse only i think

Strat games will be for the best, lemme think
(also i feel you, I cut my hand a few years ago trying to cut an apple....with the apple in my hand -_-, I dont know how i'm still alive honestly)
-Kingdom (classic or new lands, I'd say just get new lands)
-Hellenica (visual novel areas for plot and character in between turn based battle maps)
-Plague inc
-Sheltered
-Tormentum- dark sorrows
-The amber throne
-Belladonna
-Last word
-Violett

• A magical high school girl (turn based rogue like game)
  -cherry tree high series
• the silent age (point and click really really good)
• higurashi: when they cry series (really good creepy visual novel)
• corinne crosses dead and breakfast
• va-11 halla (bar mixing visual novel)
  -stardew valley
  -still life series
  Actually any visual novel would be easy to play, also any point and click game (I suggest the Edna and Harvey series), or rpg without quicktimes

I have 2 that come to mind if you enjoy space type stuff, take a look:
Astrox
Planetbase

Montaro

Battle for Wesnoth, a free, open source, turn-based strategy game with unit progression. Keyboard shortcuts are very helpful but not mandatory. Great gameplay, great graphics, great music, many single player campaigns, local and online multiplayer, tons of downloadable, player-made extensions.
Hope your hand will heal soon!

• This Is The Police
• Morphblade
• 80 Days
• This War of Mine
• Little Inferno
• McPixel
• Papers, Please
• Punch Club

If you count games playable with one hand on a keyboard, then I'd also recommend Crypt of the NecroDancer and Undertale.

Point and click games, mostly from Daedalic Entertainment. Strategy games too, turn-based obviously.

I picked up Don't Starve yesterday, no need for keyboard there ^^

Civilization series, and all games like it.

Xcom 2 can be played with only mouse. Also Prison Architect , Steamworld Heist , Cities Skylines , Oxygen Not Included , Parkitect , Rimworld and Bloodgate

Try Quest Run.

Civilization, of course!

Dead Age

SteamWorld Heist!

Super Hexagon can be played with just the left and right mouse buttons

King's Bounty series

You can play the whole of the first Witcher using only a mouse, not sure how good it is though, never tried it.

Any HOG

One Finger Death Punch!