On what operating system are you hosting your Plex Media Server? It should like your server isn’t claimed, which will prevent it from be visible on your account.
If you’re Windows, right-click the Plex app icon in the notification area (“systray”) near the clock (you may have to click the up arrow ^ to see it). Then select Open Plex. If the server isn’t claimed, this should start the claim process and setup.
If you’re on a Mac, find the Plex icon near the clock in the menu bar. Left-click it and select Open Plex to begin the claim/setup process.
If you’re on Linux with a desktop environment, log on there, open a local browser in private/incognito mode, and navigate to http://127.0.0.1:32400/web. This should start the claim process.
I’m in Windows. “Open Plex” merely opens a website, which the mirror image of the app. And does the same thing. “Get Plex Media Server”. Plex Media Server sent me to the website. Obviously I need to install it again. How many times until it works?
That makes it sound like there may have been an error in the claim process. One of the forum moderators wrote up some instructions for Windows users for the process to correctly reclaim the server:
Another option would be to just start completely over by following the directions here. There’s warning in red at the top of the article (you will lose all metadata in existing libraries, i.e., it will be like PMS was never installed): https://support.plex.tv/articles/201941078-uninstall-plex-media-server/