The issue with antibiotics for abscesses (in horse, or human, or any other species) is that usually by the time the abscess has started causing pain, the body has already walled the infection off (which is what creates the pressure). If the infection is walled off, the likelihood of antibiotics getting into and fighting it is extremely low so you (or your horse) essentially end up taking antibiotics for no reason which can equal increased antibiotic resistance with no meaningful benefit. The only way to really treat it is to open it, drain it, and keep it clean until the tissue can granulate and the wound can heal.
Source: experienced a very painful abscess of my own that I had to have drained and packed. Iāve taken antibiotics to address two additional ones after the initial experience because it alerted me to what my symptoms were actually pointing to and I was consequently able to catch the later ones very early (before they walled off completely), but your horse doesnāt have the words to be able to tell you that.