Can dizziness be caused by psychosomatic illness? Been to ENT and balance specialist. Both said they don't think I have ear problem. I do have anxiety

Dizziness. Anxiety can produce all kinds of physical symptoms, & dizziness is a very common one. Other things can cause these also, which is why physical and other diagnostic exams are done too! psychosomatic means your body and mind are connected, not that anything is imagined. The best news: relief from anxiety is possible -- cognitive behavioral therapy (& meds if needed.) meditation & yoga help too.
It could. Psychological stress can cause all kinds of physical symptoms. You can learn some stress reduction techniques, find a psychologist. Here's a blog about how we take things out on our body http://wakeupanddreamcatalyst.Blogspot.Com/2014/03/tuesdays-psychology-tips-do-you-take.Html.
Yes, possible. It is definitely possible. If you've been to specialists and have ruled out medical causes, then it's time to talk to a psychotherapist and explore whether there is something going on psychologically that you can address in therapy.