There is no reason to feel ashamed if you have to see a psychiatrist. I used to feel that way. I think everyone at some point in there lives has to get help from someone. All kinds of people see psychiatrists. Actors/Actresses, Athletes, Politicians, Moms & Dads, Kids all types of people. When you have feelings like this, try to find something that you like. Animals, sports, history, music, whatever and just endulge yourself into it.
Regarding your work issue, everyone makes mistakes. You at least understand that you did and seem sorry. That is a good trait.
Don't put pressure on yourself either. Things will work out.