I've created an api using .net core 2 and C#. I'm wondering if there's anyway to find out information about the computer or user that called the api. This is an internally used api so ideally I'd get the Windows user of where the api call came from, but if there's anything I can find out (like an IP address) I'd like to know how. If this isn't possible at all, I'd like to know so I can stop looking for a solution.
No, it's not possible. The server knows only what the client chooses to tell it, typically via request headers. However, the client can also lie, or "spoof" these headers. So, while something like User-Agent may look like it might give you some info about at least the OS/browser, all of that could be completely fabricated.
Matters are even worse with an API, as clients are typically thin, and the actual programmer or whatever connecting to your API must make a conscious decision to provide you with some particular bit of information, which most won't. A web browser typically sends certain standard things without user intervention, but even then users can change or alter what is sent.