Have you taken her back to the vet who was concerned about her soft spot? It's hard to tell from your description whether or not there is some calcification going on or tension in the fontanel and your vet is really the BEST person to tell the difference.
As for the cough, a round of antibiotics is a quick and cheap(er) way to rule things out, but there are problems with that. If the cough is caused by a virus, antibiotics are useless. Then you have the question of whether or not (if it is caused by bacteria) the antibiotic is even the correct type to treat it.
If it were me, I would ask for the X-ray and then, if that is concerning, a blood count to rule out an infection.
In the meantime, if you can video her when she's doing the breathing thing take that to the vets so they can get a better idea. It almost never fails that puppies, like kids, always seem to have diminished symptoms once they arrive in the doctor's office
