It sounds like you are going through the worst of it at the moment. Of course, I don't know what it is that you have, a bad case of the flu perhaps? Eventually, exhaustion should make you sleep. You are pretty sick right now, so accept that this is going to knock you out of doing anything for at least 3 days, possibly a week or more. It happens to all of us at some point. Tea is good, try drinking some tea. If you can't sleep, then just do something that you like, listen to your favourite music, read books, play a video game. Hopefully, at some point, you will just fall asleep.
You won't get better by willing yourself to get better so that you can get on with things asap. You will have to relax as best as possible, and let your body decide when it wants to sleep, and when it's ready to move on from this.