Is it normal to experience horrible agitation and anxiety with pristiq (desvenlafaxine)?

It's not "normal" Not in the true sense of the word normal. It certainly can happen with Pristiq (desvenlafaxine) and a number of other antidepressants as well. If you did not have severe anxiety and agitation prior to taking Pristiq (desvenlafaxine) and it appeared when first taking Pristiq (desvenlafaxine) it is most certainly a side effect of that medication. That requires immediate stopping of that medication. No, it's not normal and it is not common either.
No. These symptoms may indicate that it is the wrong medicine for you. Please call the prescribing md and stop the medication until you get direction from your doctor.