Aggrannoyed 

A state of being between slightly aggravated and quite annoyed

I am very aggrannoyed with this situation

Aggrannoyed by Kenneth Gear October 7, 2008

aggranoyed 

To be aggravated and annoyed at the same time

The wait was so interminably long that I found myself becoming more and more aggranoyed.

aggranoyed by B Wilson December 28, 2005

Aggranoyed 

When you're aggravated and annoyed - both at the same time!

Steve has made me so aggranoyed!

Aggranoyed by HeidiHeidiHeidiHo June 25, 2021