Gosh, so sad for you.
I had a similar experience recently, a first time kidder in labour, nothing happening but she was straining like mad. Vet called, delivered the dead kid, it was a big'un and presented rump first, not legs. She had a long acting AB and painkiller, seemed ok while it lasted but she was still off colour, not eating etc. I was milking her but she did not enjoy it. Then I went back to the vet for more ABs, daily injections, and a metacam but a day after the course of ABs stopped she literally dropped dead, just couldn't cope.
It broke my heart and in hindsight I wish I'd been more forceful with the vet re painkillers, calcium etc etc. but it was my first time kidding too. I might have saved her. Don't take any chances, I don't think any of those things Anke suggested will do any harm if she doesn't need them but may save her if she does.
I actually came on to post about a kid born this morning to the sort of sister of the one that died - they weren't related but got them as young kids together, hand reared. Anyway I missed the whole thing, despite getting up at 5, I found the kid up and about, dry and looking for milk, mum looks good too.
I'm not trying to boast, merely to say that my faith has been restored, my heart healed and that yours will too. These things happen, and it's awful that it's your first experience but don't let it put you off, it will be better and easier next time, you'll be more prepared.