Any movement or squeak indicates a loose head. Shafts can become loose through normal play. The extreme variations in temperature, from day to night, can cause the epoxy to break down. Check to see if your shafts match. There should be a half-inch increment between the lengths of your irons.
Woods usually have a one-inch increment, except for some drivers with extra long shafts.
These might be three or four inches longer than your 3-wood. If your shafts don't match, the playability or reliability of one club to the next could be compromised. Using a frequency analyzer will show you whether your shafts are well matched. Usually the shortest irons are the stiffest, while the longer irons are the most flexible. If you have a certain shaft that is too stiff, distance and feel will suffer, compared with the rest of your set.