You will not lose your save games if you chose the option in the uninstallation. Aside from that, you need to uninstall, there is no way to do it otherwise.
Well, I reinstalled. I assume that I haven't lost my saved games. I assume this because I'm not able to play the game anymore. Looks like now the game won't even start after the reinstall. It's probably something to do with the licensing, so I'm on the phone with EA.