It appears your backlight is not working. The iPhone 6S backlight circuit tends to blow easily, especially when folks forget to disconnect the battery prior to removing or installing a the screen. Unfortunately, this would not be a DIY fix and you would need to find a micro-solderer to do the repair.
As for repair, look locally for a reputable shop that does micro-soldering repairs. Ideally, you want to find someone local but good workmanship trumps locality. There are many shops worldwide that do this so you shouldn't have any problems finding them. Talk to them and ask how they do their work. Focus on troubleshooting, as opposed to shotgun replacement, and good practices like proper cleaning of boards once completed etc.
If you can't find one locally, then consider mail-in repair. There are several reputable micro-solderers patrolling this forum. You can click on my profile to learn more about my services, at the very least, it can serve as a data point.