What would cause frequent belching accompanied by rotten egg like smell,bad taste,nausea,vomiting?

sounds like gastritis, something upset your GI tract. You can try some yogurt a couple of times a day and avoid acidy foods like citrus, tomatoes, that type of food. Try to eat bland stuff for a few days. You can also try something like Zantac or Prilosec to shut down some of the acid pumps and see if that helps. The yogurt helps calm the GI tract down in most people.

It would be in your best interest to have these myriad of symptoms presented to a physician.
If you have not already done so, please make an appointment with your PCP and/or request a consultation with a gastroenterologist.
Best regards.