Dropped iPhone 7, screen shattered, won't turn on. HELP :(

I dropped my iPhone that already had a small crack in the corner of the screen. On impact, the screen completely shattered and has come off at the top and sides (I can peel back the screen and see the inside between the two metal plates [see picture]). It is still attached on the bottom by the home button. When I picked it up, the phone was unresponsive. Screen went completely black. I plugged it into my computer and opened itunes. It said “itunes has detected a device in recovery mode and you must restore”. All of a sudden, my phone got really hot, and I feared it was the battery. So I quickly unplugged it and took it outside to cool off.

Since then, I’ve tried plugging it into my computer and several wall-outlets with no luck. My mac no longer recognizes the device being plugged into to a USB port under “system report”. Itunes does nothing either when I plug it in. I’ve tried doing a soft and hard reset while the phone is plugged in, nothing. I’ve tried cleaning the lightning port. Nothing.

My question is, how can I get my data back (photos, text messages etc.). I don’t care about saving the phone, I just want my data back. Should I order a new battery and screen and try that? I live in a rural area with no repair shops around.