First of all it needs to be clarified whether the numbness
in your chin and your left hand is related or not. After seeing you one needs to come to a conclusion about whether it is because of compression in the neck or surrounding area. You need to consult a neurologist
and he will guide you regarding further investigation which may be required. he will also give you other medications for numbness. If the numbness on chin immediately followed dental treatment, then it could be related to it also.