
If you have the pup snug in a box in the car, and get the vet to examine it in the car rather than the surgery (mine will do this if asked!) the risk of infection will be minimal. The pup crying will be very distressing for the bitch, who you say isn't the most relaxed of new mums anyway.
But if gripe water is safe for human babies it seems a little should be safe for pups.....but I'm not a vet, there may be an underlying problem, as I've never had a pup behave like that. Very worrying for you. :(