First, yes, those are nail pops.

Second, you can learn to fix nail pops. I spent six years of Saturdays helping complete(their descriptions) home improvement nerds learn basic skills. All while they were helping build houses for Habitat for Humanity.

First, it helps to know what causes nail pops. Basically, the sheetrock(what the stuff is called before it is installed) is nailed to the wall studs and ceiling joists. What you have is ceiling problems caused by the joists moving independently of the walls or other ceiling joists.

It is usually best to remove the nails, but that would cause more damage in the situation in your pictures. If you were to wait until the nails come out more and were easier to pull, that would be one way. The other way is to use a punch and drive the nails through the sheetrock. You can fix the holes after installing screws to replace the nails.

To install screws, you need a drill---cordless or corded is fine. Then you need a dimpler. $5 at most home improvement stores. A dimpler allows anyone to correctly install sheet rock screws. For ceiling sheetrock, you need about 3 or 4 screws about 1&3/4" long for the area you need to repair. You should be able to buy a small amount at a home improvement store. You will propbably need more for future pops, since nail;s temd to keep popping until replaced.

Install a screw about a half inch from the where the nails are---in the same line. The dimpler will set the screw head just lower than the surface of the sheetrock.

Then, using drywall patch or spackle and a putty knife, simply fill the holes and smooth the surface level.

Let dry according to repair product instructions, and prime. You should be able to buy sheet rock primer in a spray can for touch up areas.

Then paint with ceiling white, also should be available in spray cans.

The hardest part of the whole repair job is getting out or punching through the popped nails.

Green lumber is a cause of nail pops; the wood shrinks and the nail is left protruding. The cure is to set the nails again and fill the dimple with compound. If you want to add insurance, catch and retain the head of the old nail with another nail adjacent to it. The new nail will not pop as the lumber is now stable.
As stated above, you could pull the nail, replace with a screw, etc., but if there is no underlying problem, my method will suffice.
Casey

Just take a knife and remove the loose stuff then hit the nail with a hammer....lightly! and add a couple nails or screws on either side and countersink.. Then spackle and sand flush. The trick with any drywall patch like that is to dimple the area ( wack with a hammer lightly) and then patch. Any repair should first be brought below the surface (dimpled) and then brought back flush with surface. I'm better at doing than saying but I hope it helps.

If you cannot drive the nail ALL the way in to the stud -- you gotta remove it -- or it will pop again. MUCH better to pull it out, even if there is a little drywall damage.

While you can use deck screws, I don't think I've ever had a sheetrock screw break because of torque. If that's happening to you, you need to adjust your drill/driver.

"While you can use deck screws, I don't think I've ever had a sheetrock screw break because of torque. If that's happening to you, you need to adjust your drill/driver."

No. If you try to pull in a nail with a regular drywall screw, it will break about every other time. And the method I described works - I have used it many times in my own home with long-term success.

All this advice has helped me. I have replaced the nails with screws. I have added 2 helpings of joint compound which are drying now. I have used shellac based primer and sanded and done things I've never done before in MY LIFE!!!
I have taken photos of my progress and when I am finished, I will post them, because I'm so grateful to all this help!

Way to go. A couple things for the future. Make sure your compound is completely dry before priming. Also, it's ok and easier to use water-based primer (after wiping off the dust from sanding.)

One final note, different ceiling paints have different shades of whiteness. (eg. behr is often much whiter than what folks have) Try to keep the repair as small as possible in case you don't match the color exactly.