It's normal to lose weight in the first trimester. Your doctor would have said something if he was concerned.
We can't tell you when you'll start showing, it's different for everyone. 13 weeks is too early to expect to be showing, most people don't pop until around 20 weeks (but like I said, it's different for everyone). I wasn't showing until 35 weeks and when I was people couldn't believe how far along I was.
Don't worry, i'm sure everything is fine.