Hi.
Thanks for your query.
Noted the history and understood the concerns.
Having burps and passing lots of farts along with feeling full yet possible to eat can be due to the following reasons:
Aerophagia meaning swallowing a lots of air without actually known it can cause the same problems and is usually due to stress and anxiety.
Gas producing bacteria overgrowth along with lax esophageal and gastric sphincter.
I would advise you the following in such a case:
Identify the foods and beverages, particularly the aerated drink and nuts of any sort that instigate or enhance the problems and stop these altogether.
Get the stool and blood tested and a course of an antibiotic,
metronidazole if there is an evidence of an intestinal infection will help you the best.
Take probiotics, activated charcoal tables, bananas and yogurt.
PPI like
Omeprazole and
Domperidone to avoid the burping.
Upper GI Endoscopy and
colonoscopy help further to confirm or rule out any other problems.