My burp that smells like rotten eggs. It is sometimes accompanied by vomiting. What can I do?

Giardia infection. Consult gastroenterologist for stool c/s and treatment. See reference: https://www.mayoclinic.org/diseases-conditions/giardia-infection/symptoms-causes/syc-20372786.
Smaller meals. You are describing symptoms suggestive of slow emptying of the stomach. This may respond to smaller more frequent meals. There are some medications which may be of help.