Ira ira (いらいら) means irritated, impatient or on edge.
The train is late, the queue is not moving, and someone is tapping their foot. That tapping feeling has a name in Japanese.
What it means
いらいら is the small, prickly kind of anger: not shouting, but impatient and tense. Things are slow, or someone keeps getting on your nerves, and you cannot relax.
How to use it
Add します: いらいらします (“I get irritated”), いらいらして います (“I'm irritated right now”). To calm someone down, いらいらしないで ください.
ふじさん、おそいです…。 いらいらします。
Fuji, you're late... I'm getting annoyed.
すみません！
Sorry!
Close cousins
むかむか is anger rising up from the stomach. かりかり is snappish and tense, ready to bite. ぷんぷん is the cute, puffed-cheek anger you see in anime: angry, but not scary at all.
In manga and anime
イライラ often appears with a vein drawn on a character's forehead, or a little cloud of scribbles above their head. If the anger is cute instead, the word is usually ぷんぷん.
Can you use it?
Yes, about your own feelings: いらいらします is honest and not rude. Saying it about the person in front of you (“you're irritated”) can sound like an accusation, so be careful.