Rat terrior with an ugly grayish lesion in the mouth on buccal side of molars

Lesion first appeared as swelling on cheek, on further inspection inside mouth my son located this mass of necrotic-looking mass of tissue on the floor of the buccal area of side teeth, with the inner cheek showing red, inflammed tissue around the lesion.

Oooh!  Nasty - and very well described.   Your vet will hopefully be able to get a look at this and formulate a plan.  I expect that a GA dental / explore, possibly with biopsies, might be needed.  Obviously I can see nothing of the patient but your vet will have more context and formulate a plan appropriate to your dog.  All the best - and please let us know what is found!

I haven't suggested any possibilities for this, and the reason is that I can't see it properly - drom this angle, there could be multiple possibilities, including hair and sludge wrapped around the tooth (but judging by the possible gingivitis behind it, I suspect that it won't be that simple), severe infection, even cancer.   Your vet will be able to make an assessment.

A better image, getting a vet appt now

Im pleased that you are getting an appointment and hope that they can get to the bottom of it for you relatively quickly.

Thankyou for the second picture; i think fingers, three dimensions and possibly tests will be needed to get to the bottom of this one.