So sorry hear about the cancer in your arm! I'm wondering if maybe the fact that you had thyroid cancer might have predisposed you to cancer in other places, rather than it being from the RAI treatment? I'm new to this, just having had RAI two weeks ago, so this is just a thought.
Of the people I know who have had RAI (which is VERY limited), one had RAI 10 years ago for hyperthyroidism (cause never determined), a lady in my church had RAI 30 years ago after having surgery for thyroid cancer, and one had RAI 8 months ago (Graves' hyperT). None of these ladies has ever had cancer anywhere else.
In my research, and like Archie said, the thyroid "sucks up" the majority of the radioactive iodine. The rest leaves the body "in the bathroom"! A book I recently purchased states, "When beta particles of I-131 are released inside the thyroid cells or cancer cells, they travel an average of 2.2 millimeters before their energy is completely absorbed by the thyroid or thyroid cancer deposit. This permits the I-131 treatment to specifically target thyroid cancer cells without bothering other nearby body cells." (The Complete Thyroid Book by Kenneth Ain, MD and M. Sara Rosenthal, Ph.D.).
Please keep us updated!