I've gotta real world plumbing problem and could use some opinions

[shadowrogue335]

Okay so earlier this evening I come home to find water all over the floor of my garage, there's a little room behind it that has the water heater and softener and my workshop in it. Well there's a sink back there that is the drain off for the water softener and the washing machine in the house that is flooded, I turned off the water and drained the sink and proceed to snake the pipe for probably a good twenty feet. Nothing came out and the sink still won't drain, I'm thinking maybe I should get a jug of Drano and try that before I go out and get a longer snake or end up having to call a plumber. So what do you guys think?