SASBT,
As someone who is both BT AND sex-addicted AND suffered a lot from mental problems, I think lust addiction, and addictions in general are not directly caused from the mental illness, but it's probably true that they are correlated.
What I mean is, if you did a survey of people who have problems with addictions, you would probably find much higher rates of psychological illness and/or traumatic events. It's not surprising. People find things that help them escape their reality and that they think will help them cope. Then the original situation passes and you're still stuck with the addiction and over time, it takes on a life of its own.
You sound like someone who, first and foremost, needs to address the underlying psychological problem with medication, therapy, or whatever else works. That is a yesod for everything. You can't address your life problems with your hands behind your back. After you feel "normal" again (not happy all the time, just normal), you will be in a position to start addressing the addictions, and any other aspect of your life that needs work. But until that happens, if you're like me, you will be overwhelmed with negative thoughts that you don't even realize are not the real you.