It is a phrase and it means "to be sick and tired of hearing something". It is used when someone tells you the same thing many times and you are fed up with it. Some people say “耳たこ” and it’s a colloquial phrase.
Meg and Amy are gossiping.
- Meg : Do you hear that? Ken's talking about his son.
聞いた？ケンが息子の話しているの。 - Amy : He's talking about his son joining an elite high school, isn't he?
一流高校に入った話でしょ？ - Meg : Yeah, that's enough. I don't want to hear him bragging anymore.
そう、彼の息子の自慢話は、耳にたこができるほど聞いたよ。
(or そう、うんざり。耳にたこができるよ。)
Ken's mom is advising him to prepare for an exam.
- Mom : Why don't you study more?
もっと勉強したら？ - Ken : I'm going to study later. I'm playing video games now.
後でする。今ゲームしているから。 - Mom : Are you confident that you will pass it?
合格する自信あるの？ - Ken : Leave me alone! You’ve told me a hundred times. It's annoying!
うるさいな！耳にたこができるよ！ - Mom : If you talk to me like that again, you're grounded.
もう一度そういう事を言ったら、外出禁止だからね。
Meg is complaining about what her mom said.
- Amy : How was Mother's day? Did you have a good time with your mother?
母の日はどうだった？お母さんと一緒に過ごせた？ - Meg : Yes, I was glad to talk to her again after a while. But, she asked me about when I will get married.
うん、久しぶりに(お母さんと)話した。でも、いつ結婚するか聞かれちゃった。 - Amy : Hmm, you're too busy to think of marriage.
んー、忙しくて結婚を考える暇なんてないのに。 - Meg : She told me that I should cut down on work and enjoy life. I've heard the question too many times and I'm sick and tired of it.
仕事の量を減らして、人生を楽しめって。いつも聞いてくるの、耳にたこができそう。