Can missing a kidney stone during an eswl procedure cause damage to the kidney? should an eswl be performed on tiny stones (like 3mm)?

A 3 mm stone should pass in the urine on its, unless it is sequestered in a calyx with tissue reaction around it. Drink enough water daily so that your urine is mostly colorless. Wish you good health!

Damage from ESWL depends on the number of shock waves and the power used and generally minimal when done by a trained Urologist. Generally 3mm stone pass by themselves and ESWL is not needed. There can be rare exceptions like a stone in a calyx causing pain. Pl discuss this frankly with your Urologist including your concerns. You can also get a second opinion.