Is there an anti-anxiety medicine that works to control severe performance anxiety (speaking on public) for one day?

Yes. Propranolol, a type of medication called a "beta blocker", has been shown to be very helpful for performance anxiety. It can be taken on an "as needed" basis. Of course, only do this under a physician's supervision. Hope this answer helped.
Yes. Several strategies including behavioral therapy and/or medication. Common meds include Xanax (alprazolam) and beta blockers.