There are a couple of exercises that the Olympic archers use for strength increase that you can start with the bow that you have now.
Come to full draw, hold a few seconds, then let down half way, then go back to full draw, then repeat.
Another that they use more for endurance is the draw & hold for 60 seconds, rest 60 seconds, repeat.
Just a few reps of both of those are difficult for most archers even with a bow much lighter than they currently shoot. They are pretty boring too.
When these get easy, you can put a couple of bands on to increase resistence. I don't know what type of bands to use since I haven't gotten that far yet.
It's important to do these with good form. The Olympic team members have a coach watching them when they do these because it is so important to maintain good form.
The others who posted about building up ALL of the shoulder muscles are absolutely right. There are a lot of little muscles that support the shoulder joint and not all of them are strengthened by shooting. Your push ups and pull ups are a great start, but google rotator cuff and AC joint exercises. You can probably find a dozen or more. Do 8 or 10 of these in addition to your other exercises and you won't have the shoulder problems that plague many of us.
Good luck,
Allen