Bad breath after a tooth extraction is not unusual and most often improves as the area heals.
One exception is bad breath that occurs 2 days after a tooth is removed. This can be a sign of a dry socket, a painful complication that happens in 2-5% of all extractions.
Sadly, if you have a dry socket bad breath won't be your only symptom. Learn more about dry socket here.
Bleeding - Bleeding of the site can cause an unpleasant taste and smell. You shouldn't use mouthwash for the first 24 hours. After the bleeding stops, slowly sipping water will keep your mouth fresher. Most dentists recommend very gently swishing with warm salt water or mouthwash after 24 hours.
You can't brush or floss thoroughly - The extraction site should stay undisturbed for a day or two and this includes brushing and flossing near the extraction site.
Pain Medications - Most prescription medicines cause dry mouth and as a result, bad breath. Stay hydrated to improve this type of bad breath.
Dry socket - If you suddenly notice bad breath or a bad taste 2 days after the extraction, you could have a dry socket. A dry socket happens when the blood clot comes out of the socket leaving bone and nerve tissue exposed.
While bad breath or a bad taste is annoying, your first priority is proper healing by keeping the blood clot undisturbed. For the first 24-48 hour resist the urge to vigorously swish, brush or floss near the extraction site.
Gentle rinsing after 24 hours is normally OK but if your dentist recommends waiting longer then wait longer.
My favorite product for controlling the bacteria in your mouth is Chlorhexidine rinse. Ideally you should use it the day before your extraction and starting 24 hours after gently swish with it twice a day for at least a week.
Chlorhexidine rinses require a prescription. Learn more about this product here.
Most extraction sites heal very quickly but there may be a concavity where your tooth was for several weeks.
It doesn't hurt but does need to be kept clean for 2 reasons.
1. You will heal faster
2. Your mouth will taste and smell fresher
Use the irrigating syringe provided by your dentist to keep food cleaned out of the extraction site.