Thanks for writing in.
I dont think that the cotton would be in place now. However, this can be confirmed only by an ENT exam using a otoscope
. The ear has a self cleaning mechanism. The itchiness seems to be related to an infection which may or may not be related to the cotton.
If the cotton is still in place it can be removed with a forceps by a ENT surgeon. I would suggest you dont try and do it yourself. You may end up injuring your ear drum