OK that must be the issue. I already got the free housing when I started current character about month now ago.If that is same thing that is.@aironey_ESO Hm, i don't remember my Level. But it was a new Character.
Did you check the crown store if you can collect there the free "A Friend in Need" Housing Brochure to start the quest?
Or you can start the quest if you read the Housing Brochure which you will find near most Banks too.
Or you can talk direct to Canthion if you find him
I hope that will help you