which is currently racing toward us at a speed of 250,000 mph.
First question: At what speed are we racing toward Andromeda ?
I think the two have a closing speed of 250,000 mph. For individual speeds you have to ask “relative to what?”
Also, everything in our region of the universe is moving toward a feature called “The Great Attractor”. This is on the opposite side of the center of the Milky Way so visible light gets blocked by dust. New X-ray observations show that the Great Attractor is a massive cluster of galaxies. We are moving toward it at around 2 million mph.