The shoulder is a complex joint in your body - there could be several possibilities for the pain. The hard part is to figure out what is the source of the pain to know the best way to relieve it.
Possible sources:
Pinched nerve in your neck - most of your shoulder/arm nerves are connected to your spine in your neck. If you are having neck alignment issues, could be the source is to fix the pinching in your neck. Sometimes stretching your neck all difference directions can get your neck to shift enough to decompress the nerve on its own. If not, if you see a chiropractor, may be worth a maintenance adjustment.
Shoulder alignment issue (not sitting properly in socket/subluxated) - if you had a bad fall where you broke your fall with your arm, or something similar, there is a chance your arm shifted in its socket which will cause tearing, and cause your arm not to move properly in the joint. If this is the case, the best specialist to see would be a chiropractor who has training adjusting extremities. They will be able to determine if this is the case and tap the bone back into the joint. Then it'll be time to let the stretched muscles heal to hold the joint properly.
Tight back muscles - if your upper back is tight, that could put unbalance pressure on your shoulder until you stretch out those muscles. If you have a foam roller, spend some time rolling your upper back to help.
Tight pecks - if your pecks (upper chest under your collar bone) are tight, that too will strain your shoulder. Best thing to loosen these would be to take a racket ball (or tennis ball) and roll the muscle.
Tight lat muscles - these are the muscles that run down the side of your body - neck, back of shoulder, side body under your arm, through your hip. If these feel tight, again, a foam roller will help loosen these. Also doing some side stretches - raise your arm over head, then curve your body to make a "C" shape - will help. For side stretches you can use a door frame if you want to lean away to increase the stretch. They can also be done laying on the floor.
Tight biceps or triceps (arm muscles tight) - hand massaging these or looking up some common stretches for these muscles can help relieve tension on the shoulder cause by these.
Muscle spasm - if the pain feels like there's a rock in your shoulder area, and massage/stretching isn't relieving it, you may have a muscle spasm. If this is the issue, those you just need to give it time for it to relax. Often muscle spasms are the result of dehydration or a mineral imbalance. First drink some extra water to ensure you are properly hydrated (if you live in the northern states, could be you are dehydrating with all the extra dry heat being pumped into buildings without realizing it). For the mineral imbalance, typically it's deficiency in phosphorous or magnesium. For a one time thing, try eating foods rich in these (common ones are raisins and bananas). If this is persistent, you might want to consider taking magnesium supplements (typically this would be the case if you are highly active - work out a lot).
Hopefully some of the above helps you self-diagnose what the source of your shoulder pain could be and give you some ideas of action to take.