When I change iphones, do I lose all my texts?

I spilt hot chocolate all over my iphone 5 and it now doesn't turn on. My friends told me that they were texting me like crazy, but I obviously couldn't get them. I ordered another iphone 5, but I'm just wondering if when I change my sim card over to my new one, does all of my texts that I haven't received yet go onto my new phone? Or do I lose them? And do you know if there's anything else I can recover or do I lose everything?

Text messages on a iphone are NOT stored on the sim, but on the iphone itself.
Maybe this helps recovering them from your broken iphone; http://www.iphone-ipad-recovery.com/recover-data-from-dead-iphone.html

The messages are not stored on the SIM. They are on the phone itself.

To transfer the texts you would have to back it up using iTunes & then restore from that back up on the new iPhone.

Unfortunately in your case you may not be able to get that backup since it can't turn on, so you could try to recover most of them through a (hopeful) previous backup.

If you have none, then there's nothing you could do.