7 month puppy had cough currently finishing up antibiotics can she go to the park or daycare yet?

your dog must be cleared by your vet before she can be around other dogs, this is for the health of your dog and other dogs.

If she is done with the antibiotics yes, however, keep in mind that what ever she may have had so may the other dogs in doggy day care.

I would keep the dog away from daycare for at least for an additional 2 weeks to be sure whatever may have been spread at the daycare has run its course. If I were your sitter I wouldn't accept the dog for that period of time. Best of luck