Bipolar is way overdiagnosed by psychiatrists. There's a "new" type, bipolar 2, that probably doesn't exist, and most likely comes about because of side effects of withdrawal from other medications. On the other hand, yes, bipolar patients can be extremely anxious. You need a good psychiatrist who will listen and understands the difference between the normal mood swings of life, especially the anxious life, and the outsized mood swings of bipolar disease. If Xanax helps, that's one sign you suffer from anxiety, not bipolar, but I certainly can't diagnose you from here.
Bipolar disorder can occur in addition to anxiety disorder. As well anxiety attacks can be a part of bipolar disorder but not the reverse. If you have moodswings or any other symptoms that you haven't told your psychiatrist about discuss it with them. A good resource (for all mood disorders) is "Depression Central".