Is there a nip for storing the media itself in the note rather than just a link to it?
Yep, but no one ever implemented a relay for it. https://github.com/nostr-protocol/nips/pull/345
If I host it on my own relay, then link to a picture in a normal kind 1 with a relay hint, will my followers see the pic on my post or does clients need to be made to fetch it as well?
They will need to fetch the picture in the relay you are hosting. But they already do that with any quote inside a kind1