IMO: Thank you for the picture of Carlton and I . formal Thank you for the picture of Carlton and me/myself . informal
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Grammar GeekGuys, formal and informal have nothing to do with it. It's case.
Take Carlton out of the picture - literally.
Thank you for the piture of I? Of course not! Thank you for the picture of me. Thus, thank you for the picture of Carlton and me.
(And myself can only be used