What do I do? How do I put explain this to my Professor?

Maybe go talk to a therapist at your college's counseling center. I know how you feel because I was d and dropped out of college for awhile. Maybe go talk to a therapist and explain everything that you have explained to us here. Perhaps the counselor could intervene for you and write a letter to your professor explaining your reasons for being depressed and also explain that you are embarred about telling her. Most profs will understand I think. Seriously, take advantage of the counselors there because they are great and also they are FREE.