Anchors are fun. Problem is the selection of various types is pretty dizzying. I'd go to a local hardware store (rather than a big box place where you can't get any help most o fthe time) armed with the screws you have and throw yourself on the guy's mercy saying "I need to replace 3 wall anchors on one end of a curtain rod
-- here's the screw size that's currently there and fits through my rod bracket. The curtain weighs approximately _blah_. What do you suggest?"
Replacing the anchor at worst is a matter of using a hammer and a punch (or a sturdy screwdriver if you lack one) and pushing the old anchors through the wall, patching the (hopefully small) resulting drywall holes with premix drywall joint compound, waiting for it to dry, and drilling holes for the new anchors, and pounding them into place.
If you don't have a home improvement book on your bookshelf, consider one. It's handy for showing stuff like this. Readers Digest has a pretty decent "New Complete Do-It Yourself Manual" that helped me with my first home, but I'm sure there are lots of others.
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