No, the free tests aren't "special". They may be named other things on the form - "free thyroxine" perhaps, or "triiodothyronine free"... something like that perhaps.
Anyway, I had forgotten when I last answered you about your cancer issues. So yes, I think the doctor's probable main focus right now is determining if you have a recurrence. Once you've been cleared - or heaven forbid, treated for it - he'll probably concentrate on getting your hormone levels just right.
I told you I don't know anything about the scan you're facing, so I probably shouldn't even comment... but I have a big mouth, so I will
. The risk of the test is probably infinitismal when compared to the risk of not discovering the possible recurrence. So if it were me, I'd have it done in a heartbeat and not let the risk worry me.
Hope that helped, at least a little.