WiFi keeps searching and icon issue
If it's just the icon giving you issues, not the connection, then try removing the icon from the menu bar, restarting your machine, and then putting it back. 

To remove the "Wifi Status" menu bar icon, drag it out of the menu bar while holding the command key.

Restart your machine. To put the icon back, go to System Preferences > Network > Show Wifi Status in Menu Bar.



If this doesn't work, then reset your Network interface, which will erase your previous configuration and set it back to default.