does Frodo truely find the peace he deserved in the grey havens?

[Inziladun]

Originally Posted by Orofarne

But if Frodo moved to Erresea, doesn't that show that he's not quite healed? It seems to me that Tolkien saw the sea as this good and powerful force, and if Frodo needed the sea, it almost proves how ill he is. Never mind, I'm probably entirely insane by now.

Frodo having lingering physical and spiritual ills from his experience with the Ring was the reason he passed "over Sea". The Undying Lands were his only hope of peace, until the end of his natural life.
The Sea itself is important in two ways: it is the 'gateway' for the Elves to find their way to the Blessed Realm, and it is also the place in which through Ulmo the Vala, the Music lives on, and can be heard clearly by those who listen.