This is epic, I can't help but laugh at your situation sorry. What you have here is pure comedic gold pal! So to para-phrase,
you worked for UPS and quit 3 weeks ago but worked a week after you said you were quitting
you want to go to a competitor and they don't believe you quit UPS
The place that everyone uses to verify employment actually verified that you are an employee
You had a job but quit. You were offered a job but they quit you. You will have to go on unemployment to make ends meet but you won't get it because you quit
Again sorry, but my favorite and probably the absolute funniest thing is:
UPS refuses to help you since you don't work here (and why should they) but yet you have been trying to prove that you don't work here for three weeks and UPS won't help. Why don't you have your prospective employer call the UPS number you called and be on speaker phone when they tell you they cannot help you because you don't work here.