Thanks for your question on HCM.
I can understand your Situation and problem.
In my opinion you are having GERD (
gastroesophageal reflux disease).
Cough is also seen in GERD, especially during eating. It is due to laxity of gastroesophageal sphincter.
Because of this the acid of the stomach tends to come up in the 
esophagus and cause the symptoms of 
belching and food coming in throat.
So try to follow these steps for better symptomatic relief in GERD.
1. Avoid hot and spicy food.
2. Avoid stress and anxiety.
3. Avoid large meals, instead take frequent small meals.
4. Take 
proton pump inhibitor.
5. Go for walk after meals.
6. Keep 2-3 pillows under head in bed to prevent 
acid reflux.
7. Loose weight if you are obese.
8. Quit smoking and alcohol if you have these habits.