The way that you use baking soda to help with tooth pain in your mouth is easy. Put about a table spoon in a glass of warm water and let it dissolve. Then put some in your mouth and move it around and gargle then rinse it out after about 30 seconds or so of swishing it around in your mouth. Baking soda has antibacteria properities that help kill bacteria and other harmful agents in the mouth.
This harmful material may be causing tooth decay and pain in your mouth. After doing this you should experience relief of the extreme pain you were having. Do this repeatedly for about 2 glasses of water and keep spitting it out after rinsing your mouth and gargling. The pain should then be going away. This is temporary but should help reduce the pain greatly until you can see a dentist. You should also do it after you eat, because the food will cause the pain to possible come back due to eating food that may be left in your mouth.