Wellbutrin is actually prescribed as an anxiety medication in some situations! However, since one of the side effects is ANXIETY, it doesn't work for everyone.
I took Wellbutrin for a few weeks, and it made my anxiety and panic attacks a million times worse, messed with my vision and light sensitivity, and made me perpetually dizzy.
However, Wellbutrin is often prescribed because it has less of a chance of causing negative sexual side effects in patients. There are plenty of other drugs you can try that have less of a chance of producing anxiety in you. If you're comfortable with taking an SSRI, you can try Zoloft (which also works for depression). There are also SNRI medications available now, but they are primarily brand-name only. Cymbalta and Effexor are two of these.
Talk to your psychiatrist and let them know about your anxiety. They should be able to help you find something that works better for your body.
In the meantime, you might want to ask about an as-needed anxiety medication like Xanax (Alprazolam) or Ativan (Lorazepam).