Even the emojis you type anywhere (in Instagram or Whatsapp) are gonna look like that to you. But don't worry the other person will see a normal emoji. It's just that since your phone's a Docomo one, these are the emojis you get.
You're gonna have to get used to this. If you're willing, you can flash a custom rom and get normal emojis back. But flashing one is kind of risky and you're gonna lose your data as well.
I know this one. I had a Docomo Xperia and it had the same style of emojis. I think it's a Docomo thing to include this style of emojis in their carrier phones. Search up Docomo emojis and you'll see a bunch of these. And no I think can't change thes...