Stiffness and the subsequent limitation of the range of movement in a joint are signs of arthritis, so you may instead have a muscular imbalance.
These can be caused by being in a certain position for a prolonged period, day after day. Do you drive, or sit at a desk for long periods?
If the discomfort is disturbing your sleep, I'd suggest trying some Valerian as it has been traditionally used for both aiding sleep and muscle tension.
During the day, our Arnica Gel could well help if applied 2-3 times. Your local Health Food Store may well have some free samples for you to try.
Regarding exercises, I'm not sure what to recommend in order to restore any muscle imbalances around the shoulder but a local physio will know.
Tell your GP how painful your shoulder pain is and ask for an appointment with a physio, as I believe it is free.