I feel like i've got a cut in my throat, i swallowed a small chicken bone the other day, i think and now it hurts when i eat?

Chicken bone: A scratch from sharp chicken bone usually heals if the bone went into your stomach an it will just pass thru the alimentary tract. See ENT if throat pain persists more than a few days

Depends on: how long ago, how severe your pain is, and associated symptoms such as fever, inability to phonate, chest pain, etc. It is unlikely that the bone perforated your esophagus, but certainly possible that it caused a superficial injury. See your doctor to be sure, especially if symptoms are severe or persistent.