So I’ll be honest, I reached out to my massage therapist (Liz Long of Prosperity Body Work) to help me answer your question. Although I’ve swam my fair share of laps in the pool, she has an extensive background in the sport. Her history includes 8 years of competitive US Swimming; 6 years as a private swim coach, including 2 years as a US Master’s coach with High Altitude Masters in Santa Fe, NM (copied this info from her website’s bio page at http://www.prosperitybodywork.com/bio.html).
Now that you know Liz’s qualifications, here’s the answer to your question from an email she sent me:
“Strengthen the whole core: front, sides, and back (crunches, oblique crunches, cobras, any core stabilization method you can find [that doesn’t cause you pain]).
Strengthen the whole leg (plenty of squats and lunges).
Also, strengthen the lats, shoulders, biceps, triceps, and traps. Any common gym routine for any of these will do [assuming none of the exercises cause you to feel pain].
Keep good rotator cuff health by attaching a therapy band to a post, bending you elbow at 90 degrees down by your side and internally rotating the arm for 30 seconds and externally rotating the arm for 30 seconds. Aim for good flexibility around the joints but avoid loss of stabilization.
Do a lot of stretches for the whole body after you warm up for at least 200yds and follow up with joint mobilizations like gentle arm circles.
If you really want to improve your swimming see a professional coach once in awhile.”
Wow, a lot of info, I know! Let me know if you’d like me to clarify anything she included in her response but I hope at least some of this helps you get started.