The 1.6kHz spike is probably not a problem. The 7-9kHz region is silibance which you can control with de-essing techniques.
One question regarding your vocal recording. How close are you to the microphone when recording? My guess is that you are too close and this is probably the cause of the excess silibance and the strong 500Hz component. Provided your room is big enough, I'd suggest trying to record your vocal with a distance between 0.5 to 1m between you and the mic. The closer you are the louder the low mids and the silibance will be. Another thing worthwhile trying to minimise excess silibance is to not sign straight into the mic but angle yourself to it at something like 15 degrees.
If your still not sure how to proceed I'd be happy to take a listen to your mix and give you an opinion as to what the problems might be. Just email us a snipet of the track as an mp3 (something like 256kbps to maintain quality) to email@example.com