I would be even more careful with wellbutrin if the main problem is anxiety, as this is an intentionally very stimulating antidepressant. When it works for anxiety it's probably because depression is the main problem and the cause of the anxiety -- a lot of us unknowingly suffer more from depression than anxiety but the anxiety just feel so much more powerful and disabling.
I had that problem on it had to.switch to wellbrutrin
Sometimes people get very stimulated by antidepressants, as they were all invented to treat depression, not anxiety. This may be a side effect that passes, or it might mean this isn't the right medication for you. Only time will tell. They can also be very sedating. It sounds like you're getting both effects. But three weeks is enough time for the side effects but usually not enough time to notice if the drug will work or not, so I'd give it a couple more weeks. If the problem persists, again, this just might not be your drug.
I have heard this could be a side effect. Do you take it at night? If so think about switching to the morning.