I play baseball myself. I pitch and play outfield. From what ur description is, the pain is throughout ur humerus bone(shoulder to elbow). Its highly unlikely that u have a joint, tendon, or ligament injury. It's highly possible that u pulled either ur bicep or tricep muscle. Those muscles extend from the shoulder to elbow. After throwin about 90 pitches one game, i strained my bicep and the pain bothered a little during the game, but it intensified throughout the day.
If u had hurt a ligament /tendon, the pain would be sharp and excrutiating(like getting stabbed by a needle). A muscle injury feels like a persistent throbbing and somewhat painful.
To heal a muscle injury which is what im guessing happened to u, follow the PRICE method for best results. Protection Rest Ice Compression Elevation. Check out
How Should I Treat a Strained Muscle?