나만 그런거야? basically translates to => Am I the only one who is like that? / who feels like that OR Is it like that only for me? (For a certain situation)
For example if you are cold but your friend is okay you can say 너 춥지 않아? 나만 그런거야? => Aren't you cold? Am I the only one who is cold OR Is it cold only for me?
나한테 그러면 안돼. Means => You can't do that to me OR You can't behave like that to be.
For an example, you are arguing with you mother and you are shouting. Then she can say 말조심해! 나한테 그러면 안돼! 나 니 엄마다! => Watch your language/words! You can't behave like that to me! I am your mother!