Thanks for the advice. I thought I would update:
Puppy made it through the night, vet said he was OK. Will definitely be more careful with him (my 18 y o sister was very tired when holding him to feed and cried for half an hour after it happened)
My sister and I have been caring for him since a few hours after he was born. Thankfully, he was only rejected after at least getting one feeding off his mom and was able to get some colostrum.
We've been keeping him in a box with several towels that are changed regularly and a heating pad (there's still room for him to crawl off if he gets too warm).
My concern about the crying was not the fact that he did it at all (he's very vocal whenever he decides it's feeding time) but the fact that he cried for five hours straight, refusing to go to sleep. Thankfully, he eventually did sleep and seems to be doing better now.
The vet gave him a pass, so we're all very relieved over here.