I am so glad I joined this site!! For years I have had ear problems and dizziness. These symptoms just seem to exacerbate my anxiety even more to the point I was constantly worried about getting dizzy or having my ears clog up (which gives me dizziness and other symptoms). I really thought I was the only person who suffered with this, but once I came here I have seen tons of posts concerning ears, dizziness, and anxiety. I have done some pretty extensive research on this and have been to an ENT specialist. The ears and Eustachian tubes can be a huge cause of dizziness. I have never tried active noise cancelling headphones, but anything that affects the ears can be a cause of dizziness, and we all know once the symptom is there...we just worry about it all the time!
I believe the way those headphones work is to emit a frequency that cancels out the noise by destructive interference. This frequency could irritate the eardrum or inner ear in some way which will absolutely cause dizziness. I notice sometimes when I am finished listening to music, even with regular headphones, I get a little dizzy for a few seconds. I would definitely stop using them and see if it makes a difference. If you are still getting dizzy, have an ENT check out your ears. I am not sure if those headphones can cause any damage or longer term side effects, but I'm sure an ear doc would know.
I too hope you find the culprit!