BF does burn quite a bit of calories but also depends on how much u are producing and it is not true for all women. For some, their bodies will store more fat for BF.
It's normal that u are sill wearing maternity clothes as it takes time to slim down.
Exercise when u are cleared for it. Walks and slow jogs. More protein, less carbo, more fiber. Rmbr to have strength training/resistance training too