The pain in your teeth coupled with the post nasal drip points to a sinus infection. The normal treatment is Antibiotics . If you don't want to do this, nasal irrigation with a neti-pot or squeeze bottle system will help you get the infection out. Once your infection is cured, your bad breath should go away, however if you have allergies, you might still have some slight post nasal drip.
When my allergies were out of control, I also had stomach problems including gas. My allergy doctor actually told me this was common, as there are actually two types of histimine, one of which is in your stomach. So allergens often cause the histimine to be released not just in the bloodstream, but the stomach also.