I'd go with the other's comments.
The blades being loose would indicate that the new blade's bolt hole is too large and, maybe, the blade is too thin.
The large nuts on a rotary mower can only be tightened so far before they run into a ridge on the bolt. This designed slight looseness allows the blade to rotate out of the way if something is hit. The fit has to be exact.
The blades hitting the sides is another giveaway that the blades are wrong. They should miss the sheet metal by 1" to 2".
My advice: Take the old blades, the new blades, the large nuts and bolts to a tractor dealer and match them all up correctly. Tractor Supply might have what you need.
What brand of "bush hog" are you working on?