Hello,
Thank you for your query at DoctorSpring.com
Skin that is falling off could be either due to a fungal infection also known as candidal intertrigo resulting from excessive sweating, where the toe around the skin is loose and flaky. It has extremely bad odor too.
Meanwhile I would recommend that you apply Clotrimazole cream mixed with Mupirocin cream twice daily on the afffected areas. This will help resolve the yeast infection.
I would also recommend that you keep your feet as dry as possible.
Please let me know if you have any queries.
Will it be possible for you to upload a picture of the greenish patch?
Based on that i can suggest further appropriate treatment for you.
Awaiting your reply,
Regards.