It definitely sounds like she is breeding. It sounds like the white thing is an egg, but you don't see one? Maybe something happened to it. It could be hiding somewhere or I've heard it's possible they will eat them. :/ I'm not sure I believe that one. But my Cinnamon was laying eggs and one time she looked like she was going to lay and then later didn't, but I couldn't find the egg anywhere. Still not sure what happened there. :/
Either way, that is definitely breeding behavior. If you do not want her to breed, she definitely should not have a nestbox! Access to small, dark, enclosed spaces, such as a nestbox, encourage breeding. It is also good to shorten her day. Cover her cage for 12-14 hours every night. Make sure the cover will not let light through. Throw it over your head. If you can't see any light, it's good. If you can, either get a different cover or throw another layer on. A couple thick blankets should do the trick. Cockatiels breed during the summer months and one thing that triggers their breeding behavior is longer days. If you shorten her day, she will think that it is not the right time to lay eggs.
For now, all eggs should remain with her or be replaced by dummy eggs. Personally, I don't see the point in dummy eggs unless they are fertile. However, it doesn't sound like you have a male. Do you? If she has a male partner and you do not want the eggs to hatch, you should replace the eggs with dummy eggs. Then, once the eggs get to about 21 days since laid and they do not hatch, she will lose interest. Then, and ONLY then, you should take the eggs away. If you take them away before she loses interest, she will just lay more to replace them.
I hope this helps! If you have any more questions, just ask!