In my experience, injuries sometimes arrive like a storm. But you will not be unlucky like this forever. You may find injury is rare later or in next season.
I know your problem is too many injuries and it will be less. But your current solution to this is still red treatment pack management. Red packs are generally used for long term injury only, especially when you feel injury storm is coming or have arrived.
The biggest injury crisis I ever faced was suffering about 12 injuries with 7 days and players are unavailable for total over 50 days. In that season, no. of my red packs is always close to zero. After this crisis, I am even more prudent to use my red packs. I am never a farmer for red packs. But my team's balance of red packs usually ranged from 160 to 200 now. My other team have even more, usually over 200. With these stocks, I am not afraid of the injury crisis I faced before. But I need to keep discipline to save red packs for long term usage.