Welcome to the community forum. 
I think you need to specify if your screen doesn’t work at all anymore or if it still properly displays and still has touch functionality.
If it’s still possible, you can call this string of characters * # * # 6 6 #* # * to get a set of almost 30 hardware tests on your FP3. This allows you to check all sorts of components.
If it’s not, the only way you can check is if there is another Fairphoner with an FP3 near you who is willing to let you test her or his display on your FP3. You might want to have a look here, although I want to say that not every Fairphone Angel might be willing (or able) to provide an FP3 display for testing: