Aside from word choice, I see major issues with the passage. I think instead of searching for the perfect single word to show varying forms of irritation (which you would doubtless plan to switch out to avoid repetition, yes?) you should start considering such rules as
· Show, don't tell!
· Tell the story from the character's point of view.
Instead of telling the reader directly that Aarii's irritated, you should trust them to be a little more perspective; throw more expressive hints in dialogue, if helpful; and do your best to show through action and thoughts. Thus I think you could do worse, in your example, than making these few changes (this presumes that we have previously set the stage for Aarii talking on the phone with her mother):
"Maybe you should think about getting engaged. Maybe even before your poor mother dies of old age, hmm?"
"Why should I get engaged? Because Bela did? I will when I'm ready, Mom."
"I know, my little shrimp-cake. Now I want you to get some sleep, and make sure that the hotel drops you--"
"Yes, of course the hotel car will drop me off. Goodbye!" Aarii slammed the receiver so hard that the phone bounced off the bed. She stared out at the falling snow [or picked her nose, or whatever] as the busy signal bleated up at her, then eventually fell silent. No way would she get engaged to Shloim, the toad, just to keep up with her overachieving baby sister!
This bit of asinine foolery (I'm incapable of better at the mo due to being a little woozy, sorry) hopefully serves to illustrate a couple of points. First, you can show irritation through such helpful measures as slamming phones, punched faces, bowling balls heaved through mirrors and the like. You've already got Aarii throwing the phone on the bed; that plus annoyed phrasings in the dialogue can work quite well enough to get the irritation across. You don't need to telegraph irritation, then follow up to explicitly, tritely beat the reader over the head with it.
Second, since you seem to be telling the story from Aarii's point of view, you should try to shorten the narrative distance and get the reader right inside Aarii's head, instead of narrating things as if you were observing Aarii from within the room. You do this by eliminating "telling" statements that have the effect of standing the reader near but still away from Aarii in the room; a common mistake is to use such phrases as "Aarii said, eyes blazing" (since Aarii can't see herself). Instead, just present things directly and as Aarii would experience them. For example, since Aarii can hear her mother's voice, it places the reader as a third-party observer outside of Aarii when you suppress the mother's words; isn't it better to simply present what Aarii hears, along with the rest of it? Let the reader be Aarii, as much as possible. This will also give you more chances to present useful contextual information that will help explain just what emotions Aarii's feeling, and why.