Please stop beating yourself up for not hearing Emer. You are a fantastic mother, and an inspiration to me (and a lot of others, from reading comments over the years).

You took steps to try to hear her crying, and they didn't work, and she was very unhappy. But: they were reasonable steps, you couldn't know in advance they wouldn't work, but you do know now; she didn't come to any physical harm; and I'm sure that as soon as you found her you comforted and reassured her as much as possible.