Aww, Brooky...
I get it. I have my own 'puppy' AKA 11-month-old who causes the same anxiety in me. He was sick this past week and awake from 12 or 1 am until 4 or 5 am every morning. We were at my parents' for Easter and did the same thing to me. I just lost it around 3:45 am and started bawling as I was rocking him and trying to get him to stop screaming so everyone else wouldn't wake up.
I kept reminding myself that it's only a phase, that it's only a couple hours of the day, that he can't realistically be awake all day and all night long, that I would get a break and be able to sleep a little once my mom woke up, etc etc etc. It's hard to be logical in the middle of an emotional breakdown, but I do my best to remind myself that facts are facts and feelings are feelings and that I should act on one and not act on the other.