A big part of your problem is not having enough depth in your team. You only have 6x reserves, but should ideally have 10 (With 1x spot free for if you want to purchase a new player).

As injuries are a part of the game, as are red cards, you're having bad luck, no doubt about that, but if you had more substitutes then getting a few injuries/red cards wouldn't effect you as much.

Also I don't know if it effects the injuries you receive or not, but it'd make sense that if a player plays 2x games every day for the entire season, that they will be more likely to suffer injuries and/or red cards.