Hmm looks like a fungal infection of some sort. Not whitespot. Whitespot looks like the fish has been sprinkled with salt.
Some gouramis can get nasty (especially at night when you aren't looking). Otherwise, perhaps it is a domination thing with another platy.
Perhaps it is being chased by something into, or through, a tight space and this is causing injuries on top of the head and to the fins. Fungus can be a secondary infection that grows on recent wounds.
I would separate it (float it in the tank in an ice cream container, bowl etc) and treat with a fungal med. These are available at pet shops.