Surprise changing fee

So I rescheduled my flight to Hunter Army Airfield 1 day early via phone and was even able to choose my seats. I asked my representative if there was a changing fee to this flight, which the response was no. 
I get to the Delta Airlines kiosk today (20-30 miles away from my residence) and they are trying to charge me $150. I spoke with a supervisor at the call center, to confirm what I was told yesterday, who explained to me that my call was never documented. I asked if they documented when my confirmation number was last input into their system or even the record of when customer service called me back because I was on the waiting list. The answers were no and no. 
As I began to give up I ask if there is a waiting list I can be put on (I reserved a seat, so there is going to be one left). "We don't offer a waiting list/Space-A" was the response. "Ma'am, what am I suppose to do now that I'm in this situation due to your agent?", "You can come back on you original flight date." Now I'm stuck with my bags and miles away from home, with no transportation until someone finishes work at 5:00PM.