SJS, there are different ways to ask a Rov. One way is, as you said, to ask for an Eitzah. When you do that, you are not bound to follow what the Rov says. There are some people who are able to be mevatel daas to the Daas Torah and will follow the Rov’s advice to the letter without questioning. This is a high level to reach and those who live this way are not harmed by it (quite the opposite, in fact). I wish I could be that way for everything.
Your last statement is utterly bogus and shows a lack of respect for Chachomim. In the example you gave, (if I was on the level I described above) I would accept the Rov’s decision on which antibiotic. And since I have emunas Chachomim, I would KNOW that the Rov is only telling me this because he knows what he is talking about. Otherwise, he would have recommended a physician I should go to for advice.
You may or may not believe this, but I personally DO take extensive medical advice from a certain Rov. At first, I didn’t tell the doctor about this, but when I eventually did the doctor told me that he knows this Rov very well (because many others who go to him take the Rov’s advice also) and that he learned a thing or two from the Rov. I assure you that in the case of a contradiction I would blindly the Rov’s decision. Ironically, the only time I was so to speak led astray was the time when the Rov told me he didn’t know the situation well enough and I should follow the doctor’s advice.