I experienced postpartum acne too, mummy, although mine was on my jawline and neck 😭 My dermatologist said the hormonal fluctuations after birth can be quite intense, and I noticed it got worse around ovulation too.
For me, it improved gradually as my hormones settled, but it took a few months. Since yours seems to respond to antibiotics but comes back, maybe it's worth discussing hormonal-related treatments with your dermatologist. Hope it gets better soon, mummy ❤️