It is possible to be sensitive to any free monomer in the acrylic of
the denture base.  Usually though this will be apparent by a blood-red
inflammation outlining the area of contact on the gum.  If the gum under
the denture is intact but the tongue is a problem, I think it's more
likely you're playing with this new foreign object with your tongue and
irritating it.
    If nothing else, return to the dentist.  There may be some rough or
sharp edges that could be causing this.

Steve