Going to NYU may be a good idea. They may even have free plans. Call them and ask. Also, NJ Medical and Dental School may be close to you.

Usually when you go to an institution, they tend to be really thorough with whole sets of diagnostic x-rays and so on. Go as an emergency and focus on the tooth.

Its hard to recommend Orajel just like that.

What I assumed is that your mom has a cavity in her tooth - if the pain is sharp, throbbing and sensitive to cold and pain last even after the removal of stimuli, the nerve (pulp) inside may be exposed. This can lead to the necrosis (death) of the pulp overtime and cause abcess. If this is the case, Orajel will not help -antibiotics like amoxicillin may be needed.

Your mom will need a X-ray  (even to extract tooth) of that area to determine what is going on.

I have seen people using counter irritant like Clove (lwang) and Clove oil too.