You shouldn't take Tamiflu unless you already present symptoms of the flu - it's not a vaccine! It's intended to stop the (normal) flu from progressing further, or to reduce its severity. I don't think it's even been proven to be effective for the avian flu, just the best thing we have right now.
As for the cyclohexane - it's bound with other stuff, so it doesn't have the same properties it'd have on its own. Wikipedia has the full structure for Tamiflu:
(3R,4R,5S)-4-acetylamino-5-amino-3-(1-ethylpropoxy)-1-cyclohexene-1-carboxylic acid ethyl ester
Thumbs down for names in organic chemistry
