Yes, ett öra, örat; flera öron, öronen. Öga works the same: ett öga, ögat; ögon, ögonen. ('eye')
I got the same thing with the listening exercise. I wrote Bina cause that is what I heard. Thankfully it was a typo.
How one would say in Swedish that someone forehead has high temperature due to fever? In English, one could say: your forehead is hot. How would this translate in Swedish. Also if one comes from freezing temperature outside, the ears often feel much warmer than usually. Then, I think, one could say: my ears are hot. Saying that they are warm does not mean the same (it would only mean that they have regular temperature). What one would say in Swedish?
Since the sentence refers to both ears, our expression says that someone is talking, perhaps, gossiping about you behind your back. Otherwise, it just means your ears are physically warm.
In England you might be told: "Somebody is thinking about you. Which ear? Left your lover, right your mother." I wonder if there is something similar in Sweden?
In America, we might ask someone, "Were/are your ears burning?", if we have just been talking about them (without their knowledge). That was the first thing I thought about when I read this sentence, but supposed the idiom doesn't really translate to Swedish :)