I also have shoulder injuries so I know your pain bro
What you can do to strengthen the shoulder, is to use elastic tubes (Pilate tubes???) and use them to do shoulder workouts to help build up the endurance on non surfing days.
Also, a thing most beginners seem to do, is paddle like crazy when they see a wave coming at them from 10 meters away. By the time the peak reaches them they have ran out of steam and actually slowed down and too tired to give that last few stroke needed to get in the wave.
If you look at the experienced surfers, a lot of the times they sit wait until the last moment, then turn around, and ONE, TWO, strokes and they are up on their feet.
I'm not saying you should try to copy this at this stage - it takes experience to read a wave correctly to pull this off, but pls do be aware of not starting your paddle way too early and run out of steam at the end.
I know your heard races, your are all tensed up ready to go on EVERY wave as a beginner, but eventually, that excited feeling will go away a little bit once you have taken enough waves, and actually, it will give you a clearer mind to commit better.