Hi @HristoM
Unfortunately you attached a screen shot from your phone, rather than a shot of your screen, so it is hard to tell what the damage is. I have had to remove the image, as it contained personal information.
In general, you should only use a soft microfibre cloth, moistened with soap and water, to clean Xperia screens. You should never use alcohol-based or similar harsh cleaners, as they may damage the screen coating and/or other components.
It's possible the cleaner you used got between the screen protector and the phone screen, and the stains you mention may be removed if you remove the protector, bit that's hard to say without seeing the damage.
Cheers
Mick
