I know exactly how you feel. So, you;re not alone, if that helps in some way.

People will be in a rush to tell you how natural and healthy a practice masturbation is. They mean well, but I've found this to be very unhelpful when it just make you feel, well, terrible.
I have dealt with the very condition you describe my entire life. Sexual thoughts and actions have made me feel anger, regret, shame, depression, etc. Nothing pleasant to be sure. Unlike you, I've always felt this way but I have taken a few steps that might help you.

I know you've said you'd feel uncomfortable talking about this with your current therapist. That is totally understandable. But if the issue persists, I highly recommend seeing a professional Sex Therapist as this is unbelievably helpful in this regard. It's not weird, it's not uncomfortable or unprofessional, these sorts of issues are exactly what Sex Therapists are around to help with.
Apart from that, you may with to do some research into a few things and see if you can relate. "Post-coital depression" is the closest I've come to finding an exact term for the extreme negative feelings following sex/masturbation/etc. Maybe give that a Google search or two?
I've come to identify with Sexual Anorexia and/or Sexual Aversion disorder. They aptly describe my relationship with my own sexual urges and from what I've come to understand, it is quite possible to become Sexually averse at ANY point in life.
"Thought Stopping" is something that I learned in Sex Therapy. Basically, it involves taking a step back from yourself when those negative feelings start to set in. Try as best you can to detach yourself from emotions and ask yourself a few questions. Do I deserve to feel this why? Have I done anything wrong? Have I hurt anybody? It's not full-proof, but I've found it helps.

I wish you the best of luck. And feel free to ask any questions, this is the place for answers. And as I said, I'm something of a lifetime expert on the matter. :P