I see two problems with the current formulation. First, 'good for' (in the sense that you mean) is a 2-place predicate, as in 'tea is good for Alice' and 'coffee is good for Bob'. Second, your formulation entails that if something is good for x, then ~(x=y). But of course x=y in some cases, since those variables range over the same individuals.
So I would formalize "What is good for you is not necessarily good for others" as follows:
∀x∀y∀z((Gxy & ~(y=z)) → ~□Gxz)
The following should be equivalent (though I'm not 100% sure). It formalizes "it's not necessary that: everything that is good for you is good for others".
~□∀x∀y∀z((Gxy & ~(y=z)) → Gxz)