I suggest going to an ENT who specializes in treating oral cancer patients. Any doctor who thinks you "may" have cancer and suggests you wait several months (in my opinion) doesnt have your best interests in mind when they are giving you advice.
Yes its possible for a tumor to not show up on a scan. If the tumor is less than 2 cm (the size of a grain of rice) it would probably get missed.
Remember surgeons cut and when its gone, its gone and cant be put back. A surgeon will always recommend surgery and radiation oncologists recommend radiation, etc. Go to a major cancer center where an entire team of specialists will work together with this and they will make a group decision about your individual case.
Good luck!!!
PS.... There are unfortunately many who have no known cause for getting oral cancer. I personally know several younger women who are non smokers, only light drinkers and
HPV- yet they have been diagnosed with OC. My guess would be 5 - 10% of all OC cases have no known cause.