Drywall - final joint compound coat
As the others have said, paint will not help your situation.  You will need to apply another coat of mud. The final coat can be applied using a 12 inch flat knife, but I personally like a 14 or 16 inch bow trowel. The idea is to have a thicker coat of mud over the tape and bevel or feather the edges out wide so you will not notice the small difference in thickness.  With a 12 inch knife, your joint should be about 16 to 18 inches wide. Push harder on the outside of the knife than on the inside/center of the joint. This will leave more mud in the center and feather the edges better. Do this on each side of the joint. 

Here is another tip for you.  For your last or final touch-up coat, mix a little extra water and some Ivory dish soap into your mud.  It will flow very easily, far less tiny air bubbles, and will sand out easy with little pressure. Never use sandpaper, use a 150 or 220 sanding sponge. Don't go crazy and strip it too much or you will expose the tape again. Smooth the center gently and feather out the edges more agressively.   Good luck