This is a tough time during treatment @jlsdaughter. It does start to improve slowly after radiation is complete. The common rinse is Magic Mouthwash dispensed from the oncologist. It is short term relief but it also helps to control fungal infections in the mouth which can increase pain. You are right, frequency is important.
I also had a script for an oral Lidocaine gel which really gives good relief temporarily but it was long enough to eat and swallow as I did not have a feeding tube.
Don't forget about basics like ice for numbing. She may not be able to suck on ice chips.....too painful, but a soft ice pack that wraps around the neck might really help. I used that every night at bedtime so I could get some sleep. I was 58 when I started treatment and now at 71 I can imagine how much harder it would be to stay strong as we go through this at an advanced age. Keep the nutrition going and encourage some exercise to keep her strength up. She is stronger than she thinks and needs to stay positive. Finger crossed for a good PET scan.
Make sure that when they see the oncologist they take a list of her current issues.