Lillith, don't beat yourself up over it. Things happen. Is there a way you could get a respite person in a couple nights a week so you can sleep without worrying about her? I did this when I was caring for my mother. Sometimes I could sleep and sometimes I couldn't, but what sleep I got helped tremendously.
You need to take care of yourself, too.
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Psalm 119:105 Thy word is a lamp unto my feet, and a light unto my path.