loss of feathers around cere and cere changing color

Hi. I have noticed that my parakeet (approx. 3yrs) has started to lose some feathers around its cere. Her cere is also changing to a blue tint. She is acting normal for the most part....appetite, playing etc. However, she does seem to be rubbing her beak on everything more than normal.

I called a vet and they suggested we try the mite/lice spray from the local pet store. I did that yesterday and she still seems to be rubbing etc. When we adopted her, the cere was a brownish color, which it stayed that color up until just this past week when it started to show a little blue.

We assumed that this bird was a female due to the cere color, but not we are not too sure since the cere is slowly changing to blue. We do have another parakeet (approx. 5mths) with her and he (the younger one) appears to be fine.