Thanks for sharing your query.
I have gone through your concern.
It seems that the pain is generalized and after checking you clinically your dentist
have not found any carious tooth or other pathology and he might have observed the tooth wear so he have asked the possibility of grinding the teeth.
As per I think grinding the teeth causes the throbbing sensation on taking hot or cold
foodstuff or cold air blow and it is and is generally overall in all teeth not the one side.
But it can possible that teeth on one side can be weared out because of unusual bitting habit but the symtms occurs because of hot or cold foodstuffs and soreness to face is not seen. Only the throbbing pain
which is not continuous.
If teeth grinding is the problem then you have to go for habit breakers and mouth-guards to avoid further damage to teeth and occlusal correction.
It can be related to impacted wisdom tooth;then it has to be treated or gingival or periodontal pockets if teeth are loose.
Also caries or the infection in the tooth can also results in swelling and soreness.
I would advice you not to take medicine just to get short term relief instead try to find out the cause with your dentist and accordingly take the treatment.
Nothing to worry. Just relax and get proper treatment.
Hope the information provided is helpful to you.