I will quote something you wrote:
"Unless you are popular, have perfect social skills, are super extroverted/social, move super fast in relationships, and have all of the right “pickup” lines, good luck with dating. I ain’t worth two ****s around women and feel like I have lost my last chance now by letting this lady pass me by."

You didn't "humiliate" yourself (although I can see you think you did) when you asked your friend out and she said she had a boyfriend. I would be extremely surprised if she viewed it as anything more than a nice invitation; regardless of whether she accepted it or not. You issued a reasonable invitation, and she gave a reasonable reason for not accepting. The minute I heard my knock-out friend had a boyfriend (and therefore could not lunch with me) I'd have said "So.....do you have any single friends you can introduce me to?" All the really beautiful women I know also have beautiful friends. However, external looks are only a small portion of the package of a good relationship (and when we love someone, they become beautiful in our eyes.)

The world is filled with nice women who would enjoy having a boyfriend of their own; I think it would be beneficial for you to spend some time with your counselor exploring what nice women are really like; how to find them; and how to ask them out.