Have you checked the Store and downloaded all the latest updates? There have been many updates to the messaging app, as well as the other "stock" apps. Make sure you have all the latest updates, and restart your phone (hold down power and volume down for about 10 seconds until it vibrates)
Also, If you've just installed the Win10 insider preview, doing a hard reset afterwards is recommended for optimal performance (Settings / System / About / scroll to the bottom and select "reset your phone").
Before you do, take a look at your backup options if you have any data that needs to be saved (Settings / Update & Security / Backup).
For your text message conversations, (Settings / System / Messaging - make sure text message backup is ON).