Hey Tex, sorry to say, you got ripped off bigtime. Your gf is right.
Those are "twists", which only work if you have coarse Afro/kinky hair. The only thing holding them together in YOUR hair is the wax. And as SE said, the sectioning is way too large.
Most locticians who work with Afro/kinky hair have no clue how to start dreadlocks on other hair types. Hair that isn't naturally textured can't "grab" and lock up when it's in twists. The person you paid is a perfect example of this cluelessness. I'm glad you only wasted $60 and not more!
Wash your hair ASAP and do a wax removal. (Read the guides here for instructions.) Don't worry about saving your dreads, because the twists will just unravel once they're washed (and you'll want to re-do the sectioning anyway), so make sure you scrub as much as necessary to get all the wax out.
Once you're sure all the wax is out, you can start your new dreads right away by going natural, or waiting a couple days for your scalp to calm down and then doing twist & rip or backcombing. Good luck!
updated by @tex: 07/09/15 11:54:45PM