Anytime someone takes in water through their mouth or nose, dry (or secondary) drowning is possible. But, it's very, very unlikely!
Dry drowning occurs when water causes an airway to spasm, making it difficult to get enough oxygen. In all my years of lifeguarding and teaching swimming, I never heard of a situation where it actually happened. It's in the news now simply because it's so rare.
Coughing can be a sign, but it's just as likely that she's experiencing some post nasal drip from having water in her nose. How is her breathing? Is it normal, or is shallow, fast, or labored? Do her nostrils look normal (or are they flared when she breathes?) Those are signs of respiratory distress, and that's what you need to be concerned about.
If you're really concerned, call your pediatrician and they'll walk you through it. Most likely, they'll ask the same questions.