If a 20 gauge Ithaca side by side shotgun serial 220098 has an 'S' over '20' stamped on top of the receiver where the barrel rests is this a Sousa Model?

From your description this appears to be a Flues model produced in 1912. Sousa guns appear to have had a lot of fancy engraving on them. The "S" on the metal on your gun does not stand for Sousa. Judging from gunbroker.com auction prices, your gun is probably worth $350 - $550, depending on condition and how badly a collector might want one.