I have a painful canker sore on the inside of my cheek. Will amoxicillin be beneficial and assist with the healing? Or will dr do something else

Canker sore. Canker sores are not an infection so antibiotics will not help them heal. It will heal in 7-10 days without treatment. Avoid acidic and spicy foods.
Definitely, no. Amoxicillin is used to control the spread of infection. Mouth ulcers are not infections. Canker sores may be painful for three or four days, but complete healing usually takes ten to fifteen days without the need of the antibiotics.
Wouldn't help. If anything, canker sores are viral in etiology, so an antibiotic wouldn't help.