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Pardon the length of this post, but it sounds like you may be very new at this, and maybe have some confusion about how all this works.
When a hen is broody, and stays on the eggs, (and they stay on the eggs constantly, just getting off the nest once a day for food and water, and to poop) that's called "setting". If she was setting on the eggs, she was keeping them at about 98-99F. So eggs kept at that temp, more than a day or two at most, I'd toss them.
If she wasn't actually setting, so that the eggs were cool most of the time, you could put them in a bowl of water and see if any float. Throw away any floaters. The rest, crack them in a bowl, one at a time, (when you're ready to use them) to see if they're ok before using them. A bad egg will look weird, and probably smell bad. If your hen free ranges and gets nice grass and other plants to eat, the yolks will be a nice, deep orange, rather than the sickly yellow of supermarket eggs. So if the only visible difference from supermarket eggs is the color of the yolk, that's ok. Any that actually froze will have cracks, longwise. You could boil those, mash them up shell and all, and feed back to her.
It's unusual for a pullet to go broody as soon as she starts laying eggs. Once a hen goes broody, she stops laying eggs for awhile, either until the eggs hatch and the chicks are ready to be on their own, or she gives up on hatching them. Was your hen really broody, or were you just going to the coop while she was on the nest laying her daily egg? If she was really broody, you must have other hens who were adding eggs to the nest every day. Or did you just not collect eggs for 20 days and then she went broody?
If you do get a roo later, and you want to let her hatch a clutch of eggs when she becomes broody again, it's best to save up some eggs and put them under her all at the same time, so they'll hatch all at the same time. Otherwise, you end up with 2 or 3 hatched, and a lot of partially developed dead chicks still in the eggs, when she gets off the nest with the first ones to hatch.
When a hen is broody, taking away the eggs might annoy her, but it won't "scare her out of being broody",
but when a hen is already broody, it's too late to give her a roo. She needs to mate with a roo before she lays the eggs, not after she's stopped laying in order to brood. After mating, a hen will remain fertile for a few weeks.
I hope this helps clear up some confusion. Good luck with your hen. What breed is she, and do you have others?