I don't think you're anything but a loving parent, who was frightened to realise her 3 month old might have been harmed, and feels awful about instinctive anger that's beyond the fair to your other little girl. You're human, and apologising to your little girl now, and saying you know you weren't fair, you just love them both so much that the thought of anything bad happening to either is frightening, but that you overreacted and you are so very sorry, is fine. All parents over react sometimes. It's a chance to teach your eldest that when we do behave badly, on rare occasions, we acknowledge it, apologise, and do better, and the sky doesn't fall in.
I'm more worried about some of the posters on here. With cruel streaks that pronounced, who knows how they speak to their children, and with the apparently off the charts levels of self deception necessary to enjoy behaving as they have done here to you while blithely pretending to themselves that they're just thinking of the child...! they can justify pretty much anything they choose to do, on the grounds that it's good for the victim/someone else. Wince-inducing, and please ignore the Dementors.
You're a good mum who had a bad moment, solely from horror at an unexpected, immediate risk to your very small baby. That's a human instinct, and you can sort it with your little girl. Extra cuddles, and clarity on you being the one in the wrong, and it will be fine.