TSX is not your image file, it’s the XML file, containing data about the tileset. Your actual tile image is probably already PNG.
Are you saying that your parser only supports embedded tileset data, and expects the TSX’s data to be in the TMX, including the location of the PNG? In that case, export your TMX file with “embed tilesets” enabled (Preferences -> General, check “Embed tilesets” under “Export Options”, then Export As… your map. Save it with another filename so that you can keep your non-embedded, easily editable working file.)