To me - either 'in' or 'on' is OK for any of those, but my preference would be 'in', including 'stitches in', except possibly 'arm', where perhaps 'on' is more natural.
I guess that fits with your 'concave' idea. But an eye is already concave, so it is 'in'.
I would also use 'in the' or 'on the' rather than use 'my'.