PDO threads are not a great option for the nose in general. There isn't enough tissue to hold the threads, so they will slide off pretty quickly. You may be able to get a non surgical rhinoplasty, consult with your doctor to see if you are a candidate!
If the thread is sticking out after more than a few months, what you have is not a PDO thread. PDO threads dissolve after about 2-3 months time, so you probably got a different type of thread. I would suggest seeing the doctor that gave you the treatment to see what they can do about it. They...
PDO threads take about one month to fully heal. While it may heal quicker for some and you could be fine after two weeks, I would suggest giving yourself a full month to recover from the threads. This way you can be sure that they are secured and the treatment area will not be as sensitive.