I also was diagnosed with Grave's disease and suffered from a significant amount of anxiety. I eventually had to have my thyroid gland ablated and placed on synthetic thyroid medicine for the rest of my life. As Dr. Gould stated, I feel that it is more of a physiological anxiety, and does resolve, but only when your thyroid levels are in the proper range. You might want to see if your levels are too high. Remember you need to find YOUR proper thyroid level and find a doctor that will help you achieve that. Many only go by the textbook levels. Hope this helps, thyroid problems are tough because you SEEM so healthy and normal on the outside. At least that's comment I got alot.
The link is through body in the following way. The hyperthyroid speeds up your whole body metabolism, and gives you the symtpom of anxiety. It is not the anxiety that is caused by the mind, which comes from having too many fears and unsolved problems in your mind that are not being addressed promply and properly enough. You may have both, and that will have to be sorted out as you are treated for the hyperthyroidism.