Check that your remote host (i.e. the web hosting server you're trying to connect FROM) allows OUTGOING traffic on port 3306.
I saw the (100) error in this situation. I could connect from my PC/Mac, but not from my website. The MySQL instance was accessible via the internet, but my hosting company wasn't allowing my website to connect to the database on port 3306.
Once I asked my hosting company to open my web hosting account up to outgoing traffic on port 3306, my website could connect to my remote database.