How about calling Delta and being honest? . Tell them what happened and apologize for being stupid. IMHO that works better than making up stories or crying or acting as if you had no responsibility. Just a few weeks ago I had to call them because I had managed to screw up something and it was all due to my own stupidity. When I told the agent on the phone that this was because I was the idiot and I was willing to pay whatever change fee was required she started laughing and eventually waived the fee