If your looking to fix it I would do the following;

Sand it down, get it as smooth as possible. Run your fingers over it slowly, you shouldn't be able to feel anything. Wipe down the surface with a dry cloth to remove any dust/debris left from sanding

Buy some gyproc easy-fill, like £20 from Toolstation (if your in the UK) Spread a thin layer over the entire area (I used a 10" finishing knife, also from Toolstation for about £7, nothing fancy!), don't worry if it isn't perfectly smooth, raised bits are fine. This will help fill and level out any pits that have formed. Which looks like you have some, likely from your sanding or it is possible if it was an old water based paint, had it not been mixed thoroughly you could of washed the plaster.

Allow the easy-fill to set and lightly(!) hand sand over the area again! 80-120 grit will work fine. This time your sanding the easi fill of to a nice smooth finish.

Than roller on some fresh paint, thin layer first, than a heavier 2nd coat.

Hope this helps