I've known some Samsung Service Centres provide a screen replacement under the 2 Year Manufacturers Warranty [ if the phone is over 2 years of ownership then it may still be worth asking ] when screen burn in has been confirmed @Rokyloreq so it might be worth asking.
In regards to screen burn there isn't alot you can do in regards to reducing it apart from seeing if tweaking screen brightness / display settings can help lessen the effect.
I wish you all the best. 
Don't worry, if the burn-in icons aren't too noticeable, you can play this video
or visit this online burn-in repair tool. Burn-in is actually a physical deterioration, a common issue with OLED screens. If it's already quite prominent, unfortunately, it's irreversible.
