Thank you for the photo.
Crossbeak is caused by a deformity of the skull and it can effect either the mandible, the maxilla, or both. Sadly, there's nothing you can do to correct it and it will continue to shift until the bird reaches 5 or 6 months of age. So your chick has a few more months to go before the skull sets and the extent of the deformity is known.
Trimming isn't recommended at such a young age because there isn't much to trim so you'll hit the quick - as you did. We've all been there so don't feel too bad about it.
Here's my CB Roo at a few days old.
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Here he is two+ years later. (He is able to feed himself mash so he's always a bit crusty.)
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His mandible is obviously impacted, but his maxilla curves down, like a parrot's, which is what I think you're looking at with your chick as well. Another common thing is 'tongue collapse' where the muscles holding the tongue in place weaken and cause the tongue to sit kind of in the throat. That happened with my guy.
Is your chick able to eat and drink without issue? Have you checked her crop after she eats?