mate, I had a season like this too... but I realized what I did and maybe this might help you too. (it could also be random chance, but I believe what I'm about to say will help)
It is VERY important to give your guys a rest during the season. Not only rotate them in on games, but also a rest from training (1-2 days when schedule permits).
I was completely oblivious to this when I started out the game, and some seasons were ok (injury wise) and others were a nightmare as you discribed... Since I've implimented a decent rotation schedule... I've been able to escape the nightmare injury ridden seasons...
I'm not saying that injuries will not happen, but at least i'm keeping them managable.
if you are rotating and resting your players... then disregard my thread...

and WOW you do have quite the situation there with your squad... isn't it fun to be the manager?
cheers!
Ashyr