Propecia will cause changes in your hormones. That is why the medication works. By lowering a hormone called DHT. Technically this would be an imbalance but this is the intent and why the medication works.
Definitely set up an appointment with a hair doctor to figure out what is causing the hair to grow back fine. Many times baby hairs grow because of lack of blood supply to the follicle. There are treatments that can help with this that the doctor can help you with.