I pulled a muscle by my left shoulder blade. What can I do forvthe pain other than using hot/cold compresses?

Pain reliever. Try tylenol (acetaminophen) and a light massage.
Shoulder blade pain. It is unusual to "pull" a muscle in this area. Probably the most common source of pain here is a pinched or strained nerve in the neck on that side. A rare cause is subphrenic abcess. You need to have this evaluated if persistent but can do neck stretches and icing of the neck to try and relieve inflammation with referred pain to the shoulder blade.