Do you have another area in which you habitually feel confident and prepared? You can try to isolate those components and then bleed them over into exam-taking.
People also have different motivations and personalities. For example, some people do exams best in a relaxed manner. Others work in a heightened state of awareness. This sounds silly, but I feel like a special forces op in exams, trying to slash through problems. Are you more motivated to dominate an exam curve or to show you're just as good as anybody else? Strategies will differ accordingly.
Lastly, it is my experience that you can practice an absolute sense of confidence. Nothing flashy - think calm, deliberate, relaxed, and very alert. It's easiest if you restrict it to a limited context, but sitting down for an exam is perfect. Compose tests in which you will do reasonably well - maybe by mixing problems you know how to do with more complex ones you'd have to tackle in a more flexible way. Go to the exam site, do the test under exam conditions, and up the difficulty over time. If you don't have enough time to prepare this way, do the same thing but don't take a whole exam. Just practice being confident for the first 5-30 minutes.
EDIT: You mentioned that you have had blackouts and are nervous with the environment. I've never tried this, but I'm sure professors would let you try practicing while they are giving their own exams. Explain you have test anxiety and ask to sit in. (I have to admit, the thought of 'practicing' a circuits final during others' calc exam makes smile. They'll be thinking who the hell is this guy, and why hasn't he ever showed up for class?)
I would also recommend listening to John Eliot's The Maverick Mindset. Take his advice over mine.