I see my friends with Xperia Z3 Compact D5833 are now receiving the update to Android 6.1 Marshmallow.
However my D5803 is still stuck on Android 4.4.4 Kitkat. (Yes I've tried phone companion)
Are other D5803 users finding the same thing?
I guess you've just got a handset tied to a carrier that doesn't yet have the update. Being an 03 handset it's pretty rare compared to the far more common 33 which has better band support.
If you want an upgrade flashing the firmare is probably your best bet. This is very simple but not without risk so you may be able to find a repair place willing to do this cheaply if you're not confident.