Post-extraction pain can be due to many reasons. But, from your description, it could a painful condition called 'dry socket', that occurs after extraction. It is basically delayed wound healing, due to various reasons.
The symptoms include bad breath, extreme pain, even an ear ache. This needs to be followed up with your dentist.
Next Steps
Seek your dentist's help to address this. He/she will place medication in the extraction site, also prescribe antibiotics & painkillers till the site heals.