I think I've got this weird arrow since I installed Ubuntu 18.04. It is annoying, because I can't click a tab in a browser which is under this arrow. And I am just worried, what that is. It is always there
This is typically the image of a (Budgie-) applet with an empty or incorrectly showing popover. Most likely one of your applets is not loading correctly.
To find out
Just look through the list of installed applets (loaded into the panel, as Budgie Settings shows), and/or run from a terminal
budgie-panel --replace&, and see if anything specifics shows up in the panel, pointing to the misbehaving applet.