To me, partner seems so much less clinical than "significant other".

Partner is good because it says nothing about gender, which is good if your partner does not conform to a gender binary, but also just if you don't want to reveal their gender either to prevent people being weirdos about it—like they often can online, especially if you say it's your "girlfriend"—or to protect yourself if, for example, you're in a same-sex relationship. But it also says nothing too specific about the status of your relationship. Are they your girlfriend? Fiancée? Wife? Something less conventional? If it's not important to the story, why not leave that detail out?