is a elastic band of skin connecting glans with shaft of penis.
it does not contain any significant nerve but frenular artery
artery may bleed severely in its injury.
so no such nerve is broken.
it will heal completely & will not hamper later sexual life.
as you were prescribed betadine
by a authorised doctor it will suffice.
but if you want you can apply soframycin
cream twice daily for 10 days.