Thanks Janet!
My first instinct was also a related family member of the Stinging Nettle! I even did a search with that but had no results.
The burns caused by this plant are much more severe than the Stinging Nettle and last much longer! The skin of the upper arm of my friend looked horrible, full of reddish inflamed bubbles. It took more than a week before it eventually and slowly cured!
The majority of the pictures of Urera baccifera from the links don't show the shiny dark green leaves, I couldn't see any visible hairs on the leaves on my plant's leaves either, there might have been but I didn't risk to come too close to inspect that!
I also think the stem had no spikes but was smooth, a bit purplish and ridged like you saw.
So maybe Urera nitida is a better candidate..
