Training shoulders hard once per week is plenty IMO.
No offence, but this statement angers me a little. It takes ZERO account of the type of training Vs techniques Vs biomechanics Vs the patients injury.
"Oh yeah, just train heavy once per week and you'll be OK".
I don't agree, sorry.
Firstly, the OP needs to accurately ascertain the TRUE nature of his injury (likely to involve supraspinatus since it was done whilst throwing - a common link). Generic injuries lead to generic 'treatment' which is far from optimal, especially for an athlete.
Secondly, he needs good, appropriate treatment, customised to the nature of the injury.
Thirdly he needs to eaxamine his shoulder musculature for weakness/incorrect biomechanics and learn to correct any issues, either by neuromuscular reprogramming (spinal reflex level actions) and/or muscular strengthening of weak muscles (most likely the RC and scapular stabilisers).
Fourthly, he needs to incorporate this into both his gym technique as well as his playing technique, so that it truly becomes ingrained.
So in summary.
1) Accurate diagnosis
2) Appropriate treatment
3) Correction of faulty biomechanics
4) Incorporation of corrected biomechanics
This sort of stuff takes a while, but with an athlete is definitely worth it, to prolong sporting lifetime.
The recreational lifter may choose to go with the generic diagnosis and treatment and forego the biomechanical assesment and correction. They will likely reinjure themselves because the root cause of the injury mechanism has not been addressed.
Of course, if the injury mechanism is from acute trauma (as opposed to the other two mechanisms of injury; repetitive micro-loading or tissue creep), then there may not be a biomechanical component. Having said that, where a once-biomechanically-correct individual sustains a traumatic injury, he or she may well develop biomechanical issues, depending on the nature of the injury and the time to treatment/injury resolution.
So, to offer a final opinion, the very least one should do is to incorporate some shoulder prehab exercises at least once per week.
Personally, I do 'prone Ys' (for lower/middle traps and rhomboids, 'facepulls', 'sword and seatbelt' exercises with a resistance band and then internal and external rotations with a cable stack, humerus in three different positions.
I won't do them all in one week, but I'll do at least 2 exercises at the end of a leg or back session, twice per week.
Aside from nothing else, working the RC muscles does seem to have some aesthetic carryover to the appearance of the shoulders. The only muscle not visible is the subscapularis; the others are visible and benefit from some direct work.