Can I wait for the swelling to subside and withdraw the ring on my own after an ingrown penis?

It doesn’t work.
When impaction first occurs, only the superficial veins of the penis are blocked and the penile skin and subcutaneous loose connective tissue are bruised and oedematous. If the impaction is not released in time, the penile oedema will gradually increase, intensifying the pressure on the penis, which in turn will lead to pressure on the penile arteries and deep veins, blocking both arterial blood supply and venous return, distal penile ischaemia, sensory loss, urinary retention, and in severe cases, tissue necrosis and ulceration, urinary fistula, and distal necrosis of the penile stricture.