I understand what you're facing, as that's how my reflux (LPR in my case) usually acts too. The only thing I don't have is the dizziness. It does make you extremely anxious to feel that choking or hard to inhale sensation. I had to ask my doctors repeatedly if they were sure that I couldn't choke to death or suffocate from the reflux, and they reassured that it's impossible. It took a long time for me to let go of that stress and worry, as I'd had the breathing trouble for 3 years before being properly diagnosed with LPR.
I too got headaches from starting on Nexium, but they went away in a week or so. Also, earlier this year, I was taking Nexium once a day in the morning, and my symptoms did come back after 3 weeks, especially at night. Now I take Nexium before dinner and Zantac at bedtime and feel great(both prescribed by my doctor). I think the Zantac works even better for me than the Nexium.
Good luck to you!