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This can be a polyp, or a bone spur secondary to an in jury that you don't even remember (such as blowing your nose). It can also be a deviated septum that you are feeling.
The specialist to see is a otolaryngologist (ENT - ear, nose, throat physician). Your primary care provider can give you a referral. If it isn't causing a problem (difficulty breathing, for instance), usually no treatment is necessary.
Since you say it's growing from the septum wall, then yes, it can be that far down. Someone would need to take a look at it for a real diagnosis.