My mom has been having bouts of shortness of breath after eating. she is 68 yrs old this lasts 15 minutes with coughing. she has had for 30 days?

Aspiration?: One possibility could be aspiration of food into the respiratory tract. She might benefit from a videoesophagogram or modified barium swallow test with an speech therapist. Other common conditions are gerd or gastroesophageal reflux. I would suggest a gastrointestinal evaluation.

Aspiration?: My biggest concern would be she could have a swallowing disorder where, when she eats some of the liquids or solids are going down her windpipe. This is not an uncommon condition, but can be due to serious underlying disease such as dementia/stroke, but can occur due to other factors. Take her to a doctor who will order a swallong study on her most likely.