Does the expanding universe model mean that our Milky Way galaxy is at the center of the universe?
Short answer: no
The expanding universe model describes universal inflation. Every spatial point in the universe is expanding simultaneously. No one thing is at the center of the universe.
People often relate this to the idea of being on the surface of a balloon. As the balloon blows up, every point on the surface gets farther away from every other point on the surface, but there is no one point considered the center.