Underrested is not a word. I understand it, but it’s not a thing.

Usually the phrase used is "sleep deprived". Meaning deprived of sleep. For example "the new baby wakes up at night and I am sleep deprived". "I worked 55 hours last week and now I am sleep deprived".

What it means is not having gotten enough time to relax and/or sleep.

You won't find it in a dictionary but there's no reason you couldn't use it - it's just a compound adjective. I would write it as under-rested though. Depending on what you mean by rest you could also use 'to be sleep-deprived', or 'to have been working like a dog'... I'm sure there are other compound words or phrases you could find.