Translation:I have a red nose.
If someone has "a red nose", it may means he drinks much alcohol.
I've heard of this happening once in India.
Or he was too long in the African sun.
Is 'czerwony nos' accusative? Do you always use accusative when using 'I have a /body part related thing/?'
You simply use Accusative after "mieć" (to have) :) Yes, it is.