Oh dear. It's great if you've never had a lonely New Year's Eve, but surely you're aware that lots of people can and do? It's one of the worst days of the year when everyone seems to be with friends/family/loved ones have the best time if you're alone.
The situation could maybe be seen as miscommunication, perhaps even overreaction, on a normal day for a cinema trip or drinks, but on New Year's eve with the weight of expectation? Yikes.
Kind of odd to invite her to something you weren't particularly likely to be doing, which is probably why she thought it was more certain than it was.
What's more, it sounds like you knew she would be, or thought she might be, "at a loose end" (translate as alone on New Year's Eve) when you invited her 'to be polite' to plans you didn't actually have. Being offered a lovely idea and then left hanging is way worse than it never having been raised in the first place.
Even if you thought she knew that you weren't too sure about the idea, she told you that she was serious about it when she contacted you for firm plans. She didn't say are you still thinking about going, she said when are WE going?
That was the time to either firm up plans to go to the fireworks and tell her the plans ASAP, or invite her to your catch up. To not get back to you when you said you would, not clear any miscommunication you thought there was up AND not invite her to whatever it was you were doing seems pretty inconsiderate, dare I say even a little cruel. You left someone you thought/knew would be 'at a loose end' unable to make alternative plans Ilest it be seen as being rude to you, ironically!), alone on a significant day, feeling like she's less important than you're other friends, and not even worthy of being introduced to them.
To top it all of, you really don't see how any of that is rude? Don't be surprised if her new year's resolution was to find considerate friends.