it is ok to wrap the handkerchief, but be careful to use only clean washed and very soft handkerchief- cotton or silk only...not any synthetic one. and if it hurts wear brief, you can avoid it.
at home try to keep it unwrapped and open to avoid any sweat there. you can wear loose boxers.
the white mark is scar formed on it .its risky to use any medicated ointments
on tht soft area. you can try massage
your penis lightly.by massaging help to increase circulation and also breaks scar.do gently 3-4 times in a day.if it hurt by bare hands, you can try with some silk matrial.
it may take upto few months to remove the scar by this, but its safe and natural way
and dont worry for marriage. you will be absolutely ok soon
i wish you best of luck