I wouldn't jump to such scary conclusions right off the bat. However I would ask a vet to see her as we can't diagnose her over the internet.

I'm not a vet or a vet tech or anything but I've worked in boarding kennels since I was 16 and the general rule of thumb we use is if it's a little bit of light blood then the dog is probably just stressed (which could be right in your case since the puppy is new). If there is a lot of light blood, or the bleeding continues for a long time then there could be a serious problem.
Dark Blood is a HUGE worry and requires a vet appointment ASAP. There are many causes of Dark blood in the stool and none of them are good.

As far as the throwing up and such, I would be concerned. Personally, I would call my vet tomorrow and tell them your pups symptoms and ask if she needs to be seen.

Ashley