I replaced drywall in my entire house and these do look like nail pops.
They are caused by inappropriate installation of the drywall.
It is not clear what the line in the picture is, could be a corner or could be a joint between two sheets of drywall that hasn't been done correctly.
The good news is that you can fix this yourself. Cut a circle around these pops and remove any loose drywall, it often cracks when the screw is over-tightened, you want to remove any cracked/loose parts. Put additional screws 1-2 inches away from the hole, the screw needs to go bellow the surface of the drywall but not so deep to tear the paper or crack the sheet. They sell drywall drill bits that will do the right depth for you:
Buy drywall mix/plasterer, (there is dry - you mix with water yourself, and premixed) I suggest premixed all purpose to keep it simple. Buy a putty knife:
And fill up small holes, 1x1in. For bigger holes get paper tape:
Let this dry. If it is not smooth enough - sand it. Sanding creates a lot of dust, use caution. Prime/paint.
Drywall at my place requires screws every 30cm (12in) around the perimeter, through the center along the length, into joist/stud as well as glue. Do not screw the tip of a corner as it will snap. I've seen new builds were builders used screw only every 30in, saves time and money, but customers later complain about pops. If you are not lucky, the sheet can fall off as well - I pulled one sheet on my wall and the whole thing came off - not enough screws.