Why would taking antibiotics increase stamina and energy?
I have never heard about this phenomenon from my patients or professors at the Medical School, but this is a possible mechanism that comes to my mind.

One of the classification for antibiotics takes consideration the effect on bacteria. Two possible effects are either stopping the proliferation (and letting the immune system to kill those that are currently present in the body) or killing bacteria directly.

The second approach is obviously more effective but has one big disadvantage: massive death of bacteria leads to the massive release of their toxins that are normally trapped within they bodies (so-called endotoxins). The symptoms you describe as "impossible fatigue" match exactly the symptoms of bacterial intoxication -- and this can increase upon the antibiotics intake.

Depending upon the bioavailability and pharmacokinetics some antibiotics might not kill all bacteria "on the first run" and the symptoms of intoxication recur several times with decreasing severity of manifestations.