I've been there, DD2 stopped breathing on me a couple times as a newborn. She had a prolonged respiratory illness that ended up causing chronic illness. It isn't a great feeling, to live in fear, I'm sorry. 
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How did I cope? I guess I took protective measures while knowing what I was doing but refusing to think about it. I never had her not on me, she napped on me, slept in my arms at night. I spent all my days literally sitting on the couch holding her, hence the high post count! If I was taking a shower then she was in someone's arms, that was just about the only time she wasn't in my arms. This was our life for many months but like I said, she was ill for an extended amount of time. Distraction was big, anything that would keep me from thinking. Eventually I did want to talk about it and work through my feelings and anxieties. And slowly we healed.Â