Manuka honey or high quality organic honey may help in healing, but for me the sugar content still burned, even milk, which has lactic acid, which can cause sensitivity, but many find it helpful. I also used organic aloe Vera juice as a swish and swallow, as well as organic virgin coconut oil as a swish and swallow, both which have healing properties. Have the doctor check for any infection like thrush, which can go to esphogus, mucositis, which can effect swallowing, pain.

Avoid acidic food, as Ingrid mentions, spicy, salted, sharp textured or anything irritating. Basically it's a bland diet. ChistineB has a post for easy eating foods.

As you mention, the swallowing can be assessed with a modified barium swallow test, usually done by a radiologist, doctor, and speech and swallow therapist.