You exactly describe what I go through every day Sarah! I am always *waiting* to pass out, and in public or at work I also make myself dizzy or light headed thinking any second I'm going to collapse and die. For over a year my mind wouldn't stop repeating the same "I think I'm going to pass out/What if I pass out/Any second I'll faint" type of phrases. It has taken a lot of willpower the last few months for me to get those sayings mostly out of my head, but it doesn't stop the dizzy or lightheaded feelings. I honestly don't have an answer for you because I don't have one myself, but you are NOT alone!
A breathing thing that I learned that is true about myself is that when I do start having the dizzy/light headed feeling, I notice that I breathing with my chest moving, which is actually a very shallow breath and can make the dizziness start. So I try to do more expansive but slower belly breaths, which is hard to retrain yourself (if you notice you do it too), but it will sometimes making the dizzy feeling a little better.