No risk, no worry
It's an outdated urban myth that antibiotics interfere with the effectiveness of hormonal contraceptives (birth control pills, implants, medicated IUDs, etc).
They do not, with the occasional exception of rifampin
, a fairly uncommonly used antibiotic
, certain staph infections, and a few others. See https://www.drugs.com/article/antibiotics-and-birth-control.html