Hi, if your Fitbit is new then I would take it back to the shop with your receipt for an exchange or contact Fitbit again and explain to them everything that you have done and that your Fitbit is only 3 weeks old & you want it investigating as they can view your app at their side. I was told this when I complained about mine not working. Fitbit eventually sent me a new Fitbit as mine was obviously faulty & yours seems the same. I think that there must be a faulty batch of them circulating. Since I got the replacement I haven't had an issue with my new one.
Good luck & I hope that you manage to get yours replaced like I did.
Sent from my iPhone