Basil, welcome to OCF! Glad you found this site. Any sore you have in your mouth that is there for 2 weeks or more and doesnt heal should be checked by a professional. Since you are a survivor, I would suggest getting checked by your ENT. I hope its nothing serious but only with a biopsy will the doc be certain what the spot is.
Base of tongue is not where you described. Base of tongue is not visible. The tongue is really much larger than what you see when you look in a mirror. The base of tongue is well beneath the surface, it is where your tongue first begins. Take a look at the graph on the following link and the base of tongue would be on the bottom of the tongue, down towards the throat.
NCI base of tongue diagram