Hi Riley,
I'm a former neuro nu rse and insomniac, so I know a bit about this from both ends.
For a start - stop googling! You can die of exhaustion but it takes months, and only happens when you're actually tortured to stop you sleeping at all. In "normal" insomnia you do actually get microsleeps, which completely remove the danger of dying of exhaustion, though admittedly they don't leave you feeling refreshed.
Think about it: if you could die of exhaustion, most first-time parents would never live long enough to have a second baby!
Actually there is one thing that's safe to google in this connection: try sleep state misperception.
Now you've got hold of the idea that you can't sleep, you're going to be in for the long haul of bad nights till you get your anxiety levels under control again. However, it won't do you any serious harm, it'll just make you feel tired and lightheaded.
All the usual "sleep hygiene" things will help a little. That's no computer or phone use in the last hour before bed, don't sleep with the TV on, get enough exercise during the day (but not too late at night), and avoid coffee, Coke and energy drinks after 2pm. You'd do better to avoid so-called energy drinks altogether in fact - those things are really toxic.
An interesting guy called bemmeh made a wonderful post on these boards a couple of years back. I just wish I could have read it 50 years ago when I was going through sleep anxiety! He gave me permission to quote him as often as I wanted to so here goes:
Partial quote from bemmeh:
...The moment I stopped struggling against insomnia it simply started going away, though not suddenly. It took quite a while. But the improvement was real from the start. Insomnia is not a thing in itself. The ability to sleep is so strong among us, humans or animals in general, that it is almost impossible to seriously alter it. Insomnia in us humans appears when we TRY (and therefore struggle) to sleep. You just need to stop doing all the things you are doing FOR sleeping and let your body and mind do whatever they want - if you sleep it's OK but if you don't, that's OK too (everybody has bad sleep for all kinds of reasons once in a while). When sleep time comes just go to bed, close your eyes, and rest. Don't TRY to sleep, as you are used to do. Just rest! If sleep comes that's OK, if it doesn't that's OK too, you haven't been very successful in getting the amount and quality of sleep you have desired anyway - that's why you call yourself an insomniac. So why keep on trying/desiring? Just let it go. Accept your reality and move on to the things in life you can control over. Sleep is not something we can control. You just need to trust your body and mind for it and stop trying to do anything whatsoever for it. Good luck!
End quote.