You may have injured the medial collateral ligament (MCL) along the inside of the elbow. It is the main stabilizer of the elbow in the bent position. Without it, the elbow may dislocate.
Microtrauma to the MCL can occur from repetitive load such as occurs during throwing activities. The ligament suffers tiny tears and starts to elongate or stretch out. The tissue loses its stiffness as well as its ability to withstand load and force during the pitching motion.
You may need to see an orthopedic surgeon for an evaluation. Tests can be done to look for instability. X-rays showing an abnormally wide joint space on the medial (inside) elbow may indicate a tear of the MCL. An MRI is often used to make the diagnosis. Changes observed in the image help identify the area and amount of damage done.
You may be able to treat the problem conservatively with rest followed by an appropriate rehab program. It takes a long time (months) but many nonathletes can eventually return to recreational play. Chronic joint laxity may require surgery to repair the damage and restore joint stability.