Congrats on your new puppy! Sorry to hear about the kennel cough, that's never a fun situation, but with antibiotics and vet care it should clear up. Unfortunatley, I agree with the above commenters: a seven week old puppy should STILL be with it's litter mates and it's mother. Where did you purchase this puppy from? To be so young, and come to you sick, is a big warning sign. I would really worry that you've purchased a puppy from a backyard breeder or puppy mill - (or from a petstore that purchased from either of these.)
It does sound like your puppy is just hiccuping, but if you are concerned, please do take your puppy back to the vet. As a first time owner, it's great to have any worries put to rest.
I'd also reccomend finding a proffesional trainer for you and your puppy. Pups that are taken too early from their mothers, tend to have a hard time learning bite inhibition and proper ways to socialize with humans and other dogs. Getting your puppy into a group class now will also help her have socialization with other puppies which is really important at this age.
And remember to have fun! Owning a puppy is hard work, but so rewarding.
"If you are a dog and your owner suggests that you wear a sweater. . . suggest that he wear a tail."
Vali (American Bulldog)
Artiro (Cane Corso)