First, welcome to the CG and have some rep for posting a map right off the bat.
As far as a 'professional map', it depends on what you mean by professional. I've seen maps in just your style used in online atlases, and in print, and they look fine and are definitely functional. It depends on what you want the map to do; is it purely a political map? Then I'd say label everything (depending on the level of detail you want, that could be only country names, or everything down to the smallest political units and towns) and call it done. If you're showing industry or trade, you might want to purchase or create some icons to use that represent sheep or timber, or universities, or banks, etc to place. If you're showing wars, you would probably want to tone down the color scheme significantly since it would most likely distract from what you're trying to represent. It really depends on what your ultimate goal is here. I will say that's one of the best Paint maps I've seen in a long while.