I know you will be so happy to get your internet again and to be able to skip the trip to the big yellow arches.
I really am sorry about your issues with your meds. It would seem reasonable that they get the paperwork from the last Dr's office and your history would clearly show. It only takes seconds to get a result from a basic drug screen and then a couple of days if it has to go to an outside lab for actual blood testing or extensive urine testing. Drug tests are basically very simple tests. You don't have to wait for anything to "grow" or things like that (like we do when they have to "grow" a culture to determine what kind of antibiotic treats a specific germ).
You could go ahead and call the office today immediatly after you have taken the test and have them make the appointment for you. I'd also sign everything and get those dr's reports to the correct people asap. This should help prevent them giving you meds with a much lower dose or something like that. I believe I would request that paperwork today and tell the office while I was on the phone requesting the appointment. You don't want to get delayed with "no openings" or other insane things and you need to tell them what you are experiencing after running out of meds. This can not be good for your body.
I do understand that each Dr has the need to test his or her patients to be sure they are not drug seekers. There are soooo many out there, but your medical files should tell everything about you and your history.
I wish you luck my friend!