We are all human.
Some of us are sick more and some of us are sick less but in this day and age we all get sick and we all take vacations.
I'll give my 2 cents here...
1. If a few days of being sick throws everything into chaos, you are probably stretching yourself pretty thin to begin with. You need to take a step back and leave time for yourself to be sick and to rest.
2. You need to communicate to your customers clearly, you are sick and you will be back when you are healthy. I realize this can be really stressful, especially if you are just starting out but I have yet to find a customer that did not understand this basic human function.
I learned from my experience (5+ years of being a freelance) that anything you communicate clearly and honestly to your clients will be accepted with understanding (within reason of course). Just try that, see how it goes.
Get well soon, rest, sleep, recharge. Do whatever you need so that your body will function at it's prime again.
Good luck!