In Cytoscape, the stringApp installs into the network search bar at the top of the Control Panel. I think this is where you are pasting/typing your list of gene symbols, which is correct. Before clicking on search (the magnifying glass icon), however, you will want to click on settings (the three line icon). Here you can specify how many "additional interactors" you want. Set it to zero and then you'll just get interactions between you original input.