How can I paint a few spots on my ceiling without it looking obvious?

Use a small container and try adding a bit of white paint to the original ceiling color, in case, it has lightened, due to age. Blend until you get close to the color. Use a small brush to paint spots. If white, then add an off-white (if aged), stir in, and try to match. Close is good enough, as most people do not spend too much time looking up...but there is always one, who does. Good Luck!

That depends. Are you using the exact same paint as the original coat? In that case go ahead and paint. If not, I'm afraid you may have to repaint the ceiling to avoid the spots from showing. Covering white is the worst.

Of course you can and you don't have to have the exact same paint. If you can scrape a small sample and take that color to your craft you can probably come up with a fairly good match from the acrylic paints section Try and match the color as best you can and get a small bottle of snow white to add tiny amounts to lighten the color if needed. And agreeing with the first answer, no one will notice if they are as you said small spots.

Make sure the paint and the finish match the existing ceiling. Get some paint chips and match, then get your paint. Paint the area needed and then feather the paint out into the surrounding area till it blends.

Not knowing what color you ceiling is makes it a little difficult. You can always paint stars, clouds, (or stencil) flowers, leaves or Walmart sells stick on mirror circles that you could stick on the ceiling.