I seriously doubt it, but the only people who I believe will have that answer for you are your doctor or a pharmacist.
I have always had minor anxiety and when i took any form of anitbiotics it would throw everthing off. 2 yrs ago i took 3 rounds one after another and ever since i have been searching every disease and felt like crap. It was hard to say if there is a underlying cause, since i still have a wide range of symptoms since that virus..who knows?
Some people have pretty strong reactions to antibiotics, especially those who don't take them much. I doubt it would lessen the effects of Prozac, but antibiotics kill of the beneficial bacteria that populate the intestinal tract, which are not only responsible for part of our immune systems but also manufacture some of our B vitamins, which definitely do affect the nervous system. Now that your program is finished, get a good probiotic from the refrigerated section of your health food store to replenish what the antibiotics have killed off.