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There are several issues that could conceivably cause pain and numbness in the area of the upper lip and side of the nose. However, regardless of the need for root canal therapy
(which I cannot dispute due to my inability to examine the diagnostic record), an infection
in a lower tooth would not cause numbness in the area you describe. Therefore, if your main intent is to treat the numbness and pain in the upper lip and side of the nose, you will need to dig deeper first in order to identify the cause.
The area you describe is supplied by a specific sensory nerve-- the maxillary branch of the trigeminal, or 5th cranial nerve. Pain and numbness could result from anything that affects this nerve along its course, from the base of the brain (the trigeminal ganglion), to the entire length of the nerve, which passes above the upper teeth in the roof of the sinus. In other words, a compression of the ganglion in the cranial base from an intracranial artery might do it, as could an infection in one of the upper teeth, or an acute sinus infection. An inflammation of the nerve could likewise cause this symptom, as might occur from a viral infection such as herpes zoster (shingles), or a neuropathy secondary to a disease state, such as diabetes or multiple sclerosis.
Because your dentist has ruled out a dental infection in the upper teeth, it is unlikely that your current symptoms are due to dental disease. (That is not to say that your dentist couldn't be wrong, but logic dictates that the search first be directed elsewhere.)
Based on your description, your complaint is most likely due to either a sinus infection or a neurological issue. For that reason, it makes sense to be re-examined by a medical doctor to further explore these possibilities, with a referral to either an otolaryngologist or a neurologist as deemed appropriate. Of course, you should proceed with your lower tooth root canal when feasible, but if your current symptoms are a priority, your medical consultation should come first.
Hope this helps...