Why is my chihuahua coughing, gagging, and snoring after eating grass?

If the age you put in, 20, is really correct I would say that you should have her evaluated for cardiorespiratory disease. Mitral valve disease in small dogs is extremely common particularly at an older age. Coughing is often the first sign of heart disease that we see. Another structural issue that occurs in smaller breed dogs is called a collapsing trachea. A chest x-ray should be considered strongly regardless of the veterinarian's physical exam findings. The consumption of grass is often associated with GI upset or nutritional deficiencies. Depending on what the condition is, medications that might be considered are bronchodilators, antibiotics, steroids, and diuretics. More information will be required however before commencing any therapy. Hope this helps.