Am I obligated to shackle myself in chains in order to fast Ramadan, despite being afflicted by a demonic touch that controls my body and prevents me from fasting?

You must always perform Ruqyah (definition) on yourself to get rid of the demonic possession (mass), and fast Ramadan (definition) without succumbing to the idea that it is a possession. You are not required to shackle yourself, but rather to refrain from the things that break the fast: eating, drinking, and intercourse during the daytime. This is achievable for you by seeking Allah's help and striving to use the legitimate Ruqyah.