Odor may come from nasal cavity, sinuses, tonsils, ior mouth, in all cases mostly from infection.
Smelly burps may be due to H. pylori infection of the stomach and some other gastrointestinal conditions.
Welcome to the forum!
Nasal odor could be felt due to the smell getting trapped in the nose due to trapped air as seen in nasal polyps, swollen nasal turbinates or due to nasal growths. It could also be due to a fungus in the nose. Sinusitis and post nasal drip is another possibility. It could also be due to a foreign body in the nose.
I would strongly recommend you to consult an ENT specialist. It is difficult to comment beyond this at this stage. Please let me know if there is any thing else and do keep me posted. Take care!