Not in front of the game right now but you can certainly change injury frequency settings in your league settings. You can even disable injuries altogether. (Edit: Typing this novella as bigsmooth was responding so thanks to them for basically saying what I was typing but more succinctly than I did.
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My sense is that you just ran into a bit of bad luck early. It should be noted that, as in real life, pitchers are more likely to get injured than position players in OOTP. There could certainly be other factors at work here too. For instance, how good your team trainer is but also the injury proneness ratings of your players. With pitchers especially it is always good to target as many durable (or even better, Iron Man) types as possible. Even normal injury proneness is likely to lead to missed playing time.
Injuries have apparently long been a source of contention around here with many OOTP gamers feeling they happen far too frequently (although some recent arguments are that frequency is fine but intensity is too high) but it seems that most data indicates that on the highest settings of injury frequency OOTP most closely mirrors real life and that most games under-represent injuries and as fans we tend to under-estimate just how much time is lost each year to injuries.
With pitching especially it pays to have great depth and several serviceable arms at AAA just waiting for the call-up to take the spot of an injured teammate.