Let's take your concept and simplify it a lot. I am standing inside a train car on a track. I am holding a gun. I shoot the gun at the front wall of the car in the direction I want to go. It is true that when the bullet slams into the wall, it pushes the car forwards a little. But what you forgot is that when I shot the gun initially, the train moved backwards a little. It is really really easy to show mathematically that these effects cancel out EXACTLY resulting in no net thrust.

Now, if I shot through a window instead of into the wall, I would indeed be pushing the car backwards over time. But that's not a reactionless drive, because we're throwing something out the back to go forward!