I have severe shoulder and neck pain after a mole fell off. Is this normal?

This isn't typical. I recommend getting a formal evaluation with a cosmetic dermatologist for after care and determine cause of pain. I recommend using silicone gel with growth factors to minimize scarring. Best, Dr. Emer

This is not a normal symptom.  I would recommend getting an evaluation.  Sometimes moles can bleed, and sometimes other lesions can actually fall off.  But the pain in your shoulder and neck is more extreme than would be expected.