Your stomach may have inadequate normal flora or friendly bacteria causing delay in breaking down the food which becomes putrified. The bacteria breaking out that food particularly protein,then produce an excess volatile sulphur (hydrogen sulphide) as its byproduct. The gas produced will be foul smelling and taste like that of a rotten egg.
Limiting intake of foods containing sulphur such as eggyolk, cabbage, garlic, etc can help a bit. High protein foods (especially nuts)consumption should be in moderated amount per meal. Regular consumption of yoghurt may be helpful. If you just started belching, an antacid containing sodium bicarbonate can give good effects.
Good luck and Happy New Year!