I'd write, "I myself am not among these fortunate parents." That is, if your meaning is "As for me, I'm not among these fortunate parents."
"I am not myself" means that you're literally not yourself, that you're feeling ill mentally (usually) or physically. ("I'm sorry I behaved so badly. I'm afraid I'd had too much to drink and wasn't quite myself.") So, your sentence could be interpreted as meaning, "I lose it mentally when I'm with these fortunate parents." Of course, perhaps that is what you intend :)
[native speaker, not a teacher]
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