I also feel shame about having problems. The message I have received over the years was that the only people who had problems were those who weren't smart enough or strong enough, those who were easy to fool, those who didn't have any sense. So clearly having a problem meant that I had failed in some way, or worse yet, that I myself was not good enough, in my very being...
I also wonder how to erase the shame tapes, chicory.
Someone here said something to me recently regarding failure and getting "slapped down" (figuratively) that really resonated w/me. She said that if a person is going to get involved in life, then sometimes she is going to fail or get a whack on the nose (again figuratively), but that this is nothing to be ashamed about. Instead, she should think of herself as a gnarly old fighting tomcat w/tattered ears and scars--some fights were won, some lost, but at least she was out there, engaging in the struggle!
I think maybe that thought could be applied here to at least some extent also.