Apologies if this is an obvious question but I'm not familiar with astronomy. Will this dwarf planet just pass through our solar system or is there a chance it will start to orbit our sun?
It looks like it currently orbits the sun.
The sun moves too a little bit, due to the pull of the planets. Maybe it's enough to make a difference?
But for interstellar objects, the answer is always "no". Unless it passes very close to some object that there's an orbital slingshot (or a collision, the odds of both are basically zero), interstellar objects always move away.
There are exceptions, of course. An asteroid passing through an atmosphere may be slowed down by friction (aerobraking), and be captured in orbit. Passing near another orbiting body, the interloper can be sped up or slowed down (gravity assist). But both of those require getting pretty close to a planet, and space is really big (citation needed), so it's unlikely that it would be captured.
Edit: Looks like I had the same misinterpretation, that it was a rogue planet rather than an Oort/Kuiper belt object.