My first awful awakening was my DM screaming for me to help as my type 1 diabetic brother was having a hypo. He was fitting which the sound of had woken her up but then the glucagen injection we had for him was faulty (this was decades ago when you have to make the fluid you injected up first and the valve of the liquid vial was faulty so we couldn't draw it up). I remember being completely confused about what she wanted me to do first, and although I managed to phone for an ambulance when asked to give details I was virtually incoherent as I still hadn't woken up properly. Fortunately this was back in the days when ambulances arrived quickly and one arrived in minutes. DB was fine within the hour. DM and I weren't!
The second one was waking up to the sound of a continuous beep wondering what is was, and then realising it was DS2's breathing monitor (he had quite a serious medical condition when he was young). I was out the bed and down the landing before I'd even stood up straight. I went into his room terrified of what I'd find. He'd just rolled off the mat of the breathing detector. He was still asleep and when I looked at the clock it was the longest period of sleep he'd ever done at that point. I didn't manage to go back to sleep though and at his next appointment his consultant said now he was moving around at night there was no point in using the monitor anymore.
So many of these incidents are awful even if you were already awake, but having to react to something before your brain is fully functioning seems to make them even more terrifying.