Kellyyouse - hi, I don't have any experience with illnesses traced back to a water heater, but I guess it's possible. The only way to know for sure would be to take water samples from the hot and cold sides and get them tested. Depending on where you live, your county or city health department should be able to direct you to the right place.
As far as cleaning out a water heater, normally it's fairly simple. Cut off the power to the heater (assuming it's electric), and close the valve that supplies water to the heater. There should be a drain valve (large, can be turned by hand) near the bottom of the unit, which should accept a standard garden hose. You can connect a hose there, route the hose to a suitable place to drain off the water, and then open the valve. You may see sediment coming out - that's normal and it's good to get it out of the tank. Once it's totally drained (which can take an hour or more), you can then close the drain valve, disconnect the hose, re-open the water supply to the heater, and let it totally fill up BEFORE you turn the power back on. Otherwise, you'll burn out the element(s) by applying power before the tank is full of water. And, since the supply water will be cold, you can expect it'll take a while to heat all the water in the tank.
I'm sure the real plumbers will post here to correct anything I've outlined incorrectly. One thing I'm not sure about would be getting air into the water lines...you shouldn't introduce any air into the hot water line by following my steps above. What you can do to make sure the hot water tank is filled and to get air out of the lines would be to go and open the hot water taps on all faucets in the house once you're pretty certain the tank is filled. Even though the water will be cold, it'll flow from the tank to each faucet and should purge any air in the lines.
I've been told you should do this probably once a year on older water heaters as a preventive maintenance thing. I hope this is helpful to you - good luck! Jim D/Heathsville, VA