stretching for swimming

I rarely stretch before swimming, in comparison to how I stretch before biking or running. 

I might do a couple couple big arm circles to loosen up the shoulders and maybe a tricep stretch or two (1. elbow straight up in the air, bicep / tricep perpendicular to the ground -- pull the elbow back with my opposite hand or 2. arm parallel to the ground across my chest, and pulling it closer with my other hand) but that's usually it.  Sometimes I even to pushups, although I'm sure that doesn't stretch anything.  I do these to warm up, rather than jumping into the cold gym pool, cold.

Have you taken swim lessons or had anyone evaluate your stroke?   Your stroke could be causing the pain and stretching might not solve the problem. 

Maybe I'm going to get in trouble, but I don't even stretch before I swim...because swimming itself feels like stretching to me. After I'm done, though, if my shoulders are fatigued, it feels good to do that one where you straighten your arm out and pull it across your body, hooking it there with your other arm...like this angry young gentleman I found on the internet to demonstrate. 

You also could have just pulled something if you're new to swimming. I am, and I had sore rotator cuffs the day after my 2nd swim. Went away in a day or two and hasn't returned with further swimming.

I agree.  Based on your use of the word "pain" rather than "tight" or "stiff", starting with some stroke analysis would be a good idea.  Most of the time, shoulder pain associated with swimming is the result of a technique issue, such as crossing over or pushing to the side or down rather than just pulling back.

I'm not a doctor, but practically an expert in shoulder pain. Because of the nature of the shoulder joint stretching may exacerbate the problem. The musculature around the shoulder keeps it stable. Stretching the muscles can exacerbate a problem if there is any instability in the joint. High elbow recovery can put pressure on the joint. Pulling with your shoulder instead of activating the core stresses the joint. 

Having your stroke evaluated isn't bad advice. If the symptoms don't go away I would see a doctor soon. 

There are little things that may help. Keeping the joint open (don't enter the water with your thumb, but with your hand flat). Muscle strength around the joint (this includes the back and chest, not just the shoulders) is almost always recommended for shoulder health.

Sorry if you already know all this.