I keep seeing a headed telling me to download andupdate to the newer version. I did that but nothing seems to have changed. How do I know what version of the itch.io client I am running?

If you go to the preferences screen of the app there's an advanced section that tells you what version you're running. If you updated the app, but are still seeing the banner on the homepage then it sounds like maybe you're still running the old version of the app, and you're not running the newly installed version. You can try uninstalled all versions of the app then reinstalling the latest. The newest version of the app looks slightly different than the previous major release, so you should notice a difference.