Save photos from a broken phone screen?

Hello, I have the following problem: I've had a small crack in my display for about a week, but nothing else was wrong. A few hours ago, one corner suddenly turned blue or black, and then it kept spreading. Almost the entire screen is now covered and unresponsive. The display is also a bit loose; you can push it in a little. It's an iPhone X, by the way. I've had problems with it before (a green stripe on the display) and had it repaired about six months ago.

Since I'm getting a new phone in a few days anyway, the phone itself isn't even the biggest problem. I'm more concerned about all the photos and data, which are really important; I absolutely need them. How can I save them? Can I put them on a flash drive at a phone store? By the way, I wouldn't want to repair the display, since I won't need it for a few days, and it wouldn't be worth it.

Thanks!