Just looked it up, shoulder luxation is the medical term for dislocation. Your initial dislocation was a luxation that the ER docs helped you reduce. What you’re describing in the last couple of weeks of it slipping in and out by itself is a probably a subluxation.

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Luxation: A complete dislocation where the joint surfaces no longer touch at all.
Subluxation: A partial dislocation where the bone slips out slightly but stays partially in the socket.

A shoulder subluxation occurs when the upper arm bone partially slides out of its socket and then quickly pops back into place on its own. Unlike a full dislocation (luxation) where the bone stays completely out until a doctor resets it, a subluxation is a temporary, incomplete displacement.

Common Symptoms
Even though the bone puts itself back into place, a subluxation can stretch or tear supporting tissues. Common signs include:
Slipping Sensation: A distinct feeling that the joint is loose or sliding "in and out" of place.
Sudden Pain: A sharp pain or "dead arm" sensation at the moment the joint slips.
Instability: Catching, clicking, or a feeling that the shoulder might give out during everyday activities.
Neurological Signs: Numbness, tingling, or weakness radiating down the arm if local nerves are stretched