I am not a fan of antibiotics. I believe they often do more harm than good and in many cases, they don’t help the symptoms. Overuse of ABs have led the way for more and more drug-resistant bugs, they indiscriminately kill good bacteria in our bodies and they can weaken our immune system because they will always expect a crutch when it comes time to do their job.
It’s likely that the infection had naturally and finally run its course. Don’t give too much credit to the second AB.
I believe a healthy gut microbiome is key to maintaining good health. There’s a plethora of studies that show ABs wreak havoc on gut biomes but the good news is that probiotics, bone broth and fermented foods, like @anon54735292 and @Shortstuff say, will help put things back on track.
In 2015 alone, approximately 269 million antibiotic prescriptions were dispensed from outpatient pharmacies in the United States, enough for five out of every six people to receive one antibiotic prescription each year. At least 30 percent of these antibiotic prescriptions were unnecessary.

Antibiotics that doctors typically prescribe for sinus infections do not reduce symptoms any better than an inactive placebo, according to investigators at Washington University School of Medicine in St. Louis.
Sorry for the rant. Make sure you stay really, really hydrated when you are sick and get ample rest. Our bodies best repair themselves when we are expending the least amount of energy. Hope you are well soon.