Hmmmm. Sounds like you are certainly between a rock and a hard place. I have no experience with pet store pets but have always read and heard they can have serious health issues. I hope this is the worst of your new baby's problems.
I too am curious as to why purchase a new puppy so close to having to travel? Even if he was in perfect health traveling with a new puppy would be a ton of work and stress on your part (i.e. potty training, feeding etc)
I know my vet offers short-term boarding for patients. Is this something you may have available?