What you describe as exhale egg taste is what is called egg burps, sometimes called sulfur burps
Egg burps are caused when your body expels the hydrogen sulfide gas produced when certain proteins break down in the digestive system .
If your egg burp ,is accompanied by nausea or vomiting beside the pain you are describing ,this could be serious it may be an infection in the gastrointestinal tract .
BUT if you only suffer from egg burp and some sharp pains ,this will be due to the huge meal yo eat and what you eat .
These smells are produced by the breakdown of protein, complex protein foods may lead to egg burps. This would include red meats, eggs, dairy products ,garlic, onions, cabbage, asparagus ,broccoli.
If such case happens always coffee and colas should also be avoided to some extent. Fruits like cashews and bananas are known to trigger sulfur burps as well. Avoid or reduce your intake of these foods to decrease the chance of egg burps.
>>Eating very heavy meals full of complex proteins since these foods will sit in your stomach for longer periods allowing the sulfide gas to build up. Eat slowly and chew each bite thoroughly so that the digestive process begins in your mouth as it is intended to do.
So to reduce these feelings ,try to eat wisely ,eat a well balanced food
if this happened to you more often there is an over-the-counter medication that may be effective in fighting egg burps, Pepto Bismol works by binding with the sulfides in your stomach and digestive system
Remember that if these symptoms are accompanied with diarrhea nausea and vomiting beside abdominal pain check with a doctor this might be gastrointestinal infection and you will need treatment.