Hi,
Welcome to health care magic,
Burping or belching is way of body to expel out air from stomach whether it is due to excess swallowed air or produced because of food digestion or
acid reflux or gastritis etc.
During deep breathing some amount of air get swallowed in stomach through esophagus.
You should take a deep breath and it must be taken with your nose only because even slight open mouth will allow the air to get swallowed and lead to belching.
Eat high protein and easily digestive food rather than carbohydrates or fatty foods.
Drink much of water will reduce belching.
Runny nose could be due to rhinitis (allergic or infective),sinusitis,
common cold.
It is mostly due to viral infection because of low immunity but no need to worry about it as it can be easily managed by taking over the counter antihistamines like cetrizine.
Consult gastroenterologist if there is any underlying stomach problems like
hiatus hernia,
reflux esophagitis, gastritis, gastric ulcer.
Regards,