What is causing lightheaded and the heavy taste of salt in my mouth?

Hard to say. There are many causes, so if this is of concern, talking to your doctor may be the best way to sort out what is going on.
Maybe sinus problem. Post-nasal drop associated with nasal allergies or sinus infection may cause a salty taste in the mouth. Dehydration may also chase the saliva to taste salty if you are not drinking enough water. Excessive tearing, which normally drains through the nose, will also taste salty. Other exceptionally rare causes might include migraines, epilepsy or some types of brain tumors.