I think I just "lost" my mucous plug. After how long will labour start? This is my first baby.

Does your mucus plug comes with blood? If yes your labor will kick start soon, probably within few days to 1 week. For me, once I saw the bloody show, I immediately feel strong contraction pain and head to hospital for delivery. If you are worried, you can take a picture of the mucus discharge and show it to gynae if it is indeed a mucus plug and gynae will also do a vaginal examination to see how many cm you have dilated to estimate how likely will your labor start.