Both of mine had antibiotics! DS1 I had an emergency section, he was swimming in meconium. Whisked straight off to SCBU and didn't come back for over 24 hours. Bloods showed raised infection markers so 10 days of two types of IV antibiotics. I had 48 hours IV followed by two courses of oral antibiotics.
He is now 4 years old and absolutely fine! Just started school and happy and healthy. No asthma, no allergies, no eczema. I did breastfeed him for 18 months, not sure if that made any difference!
DS2 was an elective section. Fine at birth but developed jaundice and struggled to gain weight. Back into hospital on day 3. Blood gases showed raised blood sugars (which can apparently indicate an infection) so straight on to antibiotics. Culture showed no infection so they were stopped after 3 days.
Tongue tie division sorted weight gain (it was very severe). Jaundice was prolonged but he was checked at the hospital a few times and levels were ok. Cleared fully at about 9 weeks.
DS2 is now 18 months and healthy as anything! Also no allergies, asthma or eczema (certainly nothing that's shown up yet anyway!) Says loads of words, climbs on everything and sharp as a pin! Still breastfeeding so again, not sure if that helped.
You're in the eye of the storm at the moment. I've done it twice and it will be fine, you'll get there. Don't second guess yourself, you've done the right thing. Take care.