How was it that they showed you to clear it? I am surprised that they keep it in as long as they do, but then again each surgeon is different. I had 2 tubes in the duration of my hospital stay, when they cleared them they would take a bic pen and pinch the tube between their thumb and pen and then pull in short sections as far as they could and release slowly and the one time it was sort of plugged with a large clot, it got it to come through. It was painful and I cried out but it got it going again nicely. When the removed them I had one that sealed and didn't weap at all and the other that I had to change the gauze on every half hour, so if you have to make the drive home after, ask them if they can give you some gauze and tape to be safe.
Best of luck though and I hope that they will remove it for you too, they are horrible things to have to have in. Also, be sure to take some pain meds before going in to have them removed, that is extremely uncomfortable as well.