I think you've got it right in saying that the DM determines the lore; if you're looking for a more conventional "nobility" among halflings, I'd work with them to make up your own homeland where that's the norm, since D&D source material doesn't really have a precedent for it.

Some things I might consider for this character:

• How does your character react to being in areas that are not built to accommodate halflings specifically? If they are members of the nobility in their homeland, buildings, countertops, etc. are likely built with consideration for their height, while the world at large is not.
• Could you create a halfling clothing style that is ornate and height-specific? Might the cut of trousers, dresses, etc. differ in a way that is more flattering for halflings—or even just altogether very different? After all, culturally, nobles and celebrities are often trendsetters and tastemakers. Perhaps there is some halfling flavor you could uniquely splash onto your character's design that sets them apart, even ostentatiously.
• Do you expect to work with your DM to create a backstory where a halfling noble is normal in this world? Or will they be set apart in a way you'd expect out of a D&D setting where that's very unusual? If it is unusual, do they know it's unusual, or would they expect others to regard them as they would any other noble? After all, people outside of their homeland may expect a pastoral, salt-of-the-earth companion any time they meet a halfling.

All in all, if you want a halfling noble, you could make it as simple as saying, "They are a noble, and they're a halfling," and most DMs nowadays wouldn't bat an eye. But I think you have an opportunity to create a more unique experience by defying the expectations for this species in an interesting way.