'New ones'! Hilarious. FWIW I've fed 3 babies, I'm 43 and biggish busted, and they aren't broken! If they dropped a bit, they still wouldn't be broken, but they haven't, they are still as perky as they ever were!
Babies can super flexible if you want. I returned to work when DD was 15 weeks old and she bottle refused. Sipped water in my absence but took all her calories when I was there. DS's have both been boob monsters but not remotely fussed about spending time with daddy if I'm not there.
Likewise feeding in public, I've fed in so many places and apart from when they are teeny tiny, when I've barely left the house anyway, I have no need to 'whack them out' in public. The right clothes and voila, fed baby, no nudity. I couldn't be arsed with making feeds and carrying paraphernalia everywhere, it's great to be able to stick on some boots and walk out the door.
My closest friend has terrible OCD contamination fear and could only BF. Trying to prepare formula safely made her suicidal. Swings and roundabouts.
Anyway. The point is your baby, your body, your choice, but given that you've not been a mum yet, you probably don't know how it will feel so try not to get too hung up until you've tried it. That way you're not sticking a load of pressure on yourself and getting in a state if things go wrong.