Both are correct English, and the difference in meaning is quite subtle. To "feel shamed" implies a more public dimension. I could "feel ashamed" with nobody else knowing about it. I might be the only person who knows that I did something wrong, but inside myself, I feel ashamed about my actions. But to "feel shamed" implies that I am also publicly humiliated. Others know what I have done and my reputation is damaged.

Shame is generally used as a noun wheres ashamed is typically used as an adjective. Shame is the actual feeling ( an affect or emotion) which is considered to be a painful one while ashamed is feeling shame itself.

When you are shamed you are publicly made to feel bad about yourself or something that you have done or said. when you are ashamed you feel bad or guilty about something you have said or done

Feeling shamed is when someone is trying to make you feel ashamed. To shame is also a verb - "She shamed the politician". It means trying to make someone feel that emotion. When you're ashamed, like the other commenter said, it isn't necessarily social.