He's not sick at all. That white is iridescence, try looking that up. Iridescence is what makes a fish shine and pretty much every fish has some sort of iridescence unless it's been selectively bred out of them but that's difficult to do. And yes all that blue on him is also iridescence as well.
Colors on Betta's happen in layer's, so different colored Betta's actually have different layers. Blue is the top layer, then stripping down it goes to black, red and then yellow so it's like an onion (Shrek reference
) lol, or a parfait if you prefer lol. And then iridescence is the very very top layer over blue that makes a fish shiny. And it will also become dull when a fish is stressed and then become really bright when a fish is content again.
EDIT: and you'll know when your fish is sick usually. Ich are little white cysts that attach themselves to the fish, if you google it, you'll see pictures of white dots on fish. That's Ich, also known as White Spot disease. Fairly simple to care for as far as diseases go. But the general signs can be found in one of our sticky Articles in the Betta Emergencies, Illness and Disease section. Should be one of the ones at the top; Common Betta Illnesses I think and it gives a list of sicknesses that you can read on and then google them to get more information on them and how to successfully treat them. That's what I did at least and then just talking with people gave me more ideas of what to do ^_^