When you are putting the wheel back on, try lifting the front end by the two sides of the quick-release (nut and lever). This will help to set it into the fork correctly. If that doesn't work, flip your bike over like someone else suggested.

The problem is most likely that you have the wheel in crooked, where one side of the quick-release is just a little higher/lower than the other side. This small difference becomes much larger by the time the wheel gets to the brake pads.