It strikes me that a big part of the issue might be you conflating your core belief thinking patterns with your functional thinking patterns. I know, for myself, I developed a coping system almost 30 years ago, and it has to do with two things: an enormous amount of partitioning, and a deep acceptance of my 'wrongness'.
.. the second - which is this acceptance of my wrongness (I don't have a better word for it, it basically could translate as "I am completely unlovable, I am a mistake, I am a monster") - that's the core belief part, and that is not a very helpful side of my coping. It is very maladaptive, but it's a huge part of how I have gotten through my life. It would always cause me pain, sometimes, but most of the rest of the time it was how I shut down my pain - because it was a reason for feeling the way I did. Of course I was deeply sad, monsters are probably sad. Accept it and move on.
It's filtered into my life in a very tangled way, and ultimately, it's where I hit the wall with CBT, . my sense was that I could spend 12 hours a day, every day, doing thought records and I'd never even keep up with the daily negative thoughts, let alone getting to their origins.. So, putting more focus on the trauma processing itself, and just continuing to identify and challenge that negative thinking, but also recognizing that it's likely not going anywhere until I've dealt with the trauma....that's what has made it doable for me to be working on all this stuff.
I think this is very wise above, what @joeylittle said. I think that is why ptsd can feel 'not' like a mental illness, in so far as we continue to think, or feel or function in ways which do not seem to be influenced by anything other than rational thought. You hear that here a lot (& I've said it to myself- "just get over it".)
The bad thing about self-beliefs (speaking for myself) is that I feel like I have sufficient & irrefutable evidence to draw the conclusions I do. Then I reinforce them. So for example, having low worth I treat myself in certain ways that I never would another I value. And I do it over & over when we believe it it has passed the point of 'fearing it' or 'wondering if it's so'. Like my abused dog, she wouldn't eat (originally). That being said she wouldn't have eaten even if I had put a steak out & left, it no longer mattered if she was assured no one was there. (In fact, it took the opposite, a few days of hand feeding & countless opportunities of love & fun & seeing nothing bad would happen.) Over & over for myself I mistreat my self in ways that reinforce the same. Even things like not making eye contact etc have bigger reasons. So as Joeylittle said, it's back to addressing the trauma that started the beliefs.
To add, I do think we 'feel' humiliated etc revealing much of stuff. I don't think that references to our intellect or ability to 'think' intellectually at work, but the emotions & trauma +/or even re-enactment of it (or attempts to bear with it or solve it on our own) impact all areas, like Joeylittle said. I think addressing it that way will help @theshadowoftheliving. I think going through the humiliation, fear & shame is part of what they mean of the necessity of going through it.
Dear @joeylittle, I hope it's ok to say, @shell described the potential roots of the exact feeling/ beliefs you described (I have them too), in a thread I posted. I don't want to paraphrase her in fear I won't do her justice, but she said it's to avoid the pain of rejection & abandonment.