Puppy is vomiting

It's possible that the chemical those pads are impregnated with is reacting with her system.  However, it is also possible that part of it has caused an obstruction.  Usually you don't see nausea from an obstruction until about 12-24 hours later, but given this history I would get this dog seen by a vet as soon as possible. 
 
Is it possible in ANY way that the dog ate something else at the same time??  Puppies will snag THE most unlikely objects -- from a knee-hi stocking to aluminum foil and beyond.
 
In brief -- when a dog obstructs on something, the stomach becomes blocked and nothing can exit it.  ANYthing that is in the tummy (even if it has backed up from the intestinal tract) will cause stomach acid to pour into the body and nausea results.  That's one of the many reasons it's so important to keep track of a pup 24/7. 

I'd at least call the vet and explain what happened.  It's possible they will be familiar with the brand of pad and know if it is something to be concerned with as far as chemicals.  I'm sure your puppy isn't the first one to do this.  And, you can never be too careful with a dog that young. 
 
Good luck, keep us updated. 

I don't think that the puppy ate anything else because we always superwise her. When she ate parts of the pee pad she was in her crate while we were out.Other then that she is always on a 6foot leash in the house directly were we are so we know what she is up to. She did have 4 poops today which were normal consistency but lots of grass in it.

Aha!! Key information is that she's pooping.  They don't 'poop' when they are obstructed.  However, just ingesting that chemical in the pads (and any urine that might have been in there as well) may have made her royally sick. 
 
You'd be better off leaving NOTHING in the crate -- messier to clean up but safer.

yeah I guess we learned that lesson[] She is doing better, she started eating again with big appetite and she drinks a lot. however she is still "coughing". If that isn't away by tomorrow I will take her to the vet.