Hi @BrooklynStar hang in there. Not sure about the coughing but just want you to know when my girl was a pup she threw up all the time (seemed like it anyway). Is there anything new in the house that could have stressed him out? For example when we moved homes Poppy was a wreck. But it could be something as little as a family member being away. Just throwing ideas out there since nothing is new for him and I know you haven't taken him outside yet. Could just be a fluke. Don't worry too much yet, he will sense your stress.
Let us know how the vet goes!