Just to give you a rough idea. I commute about 14km every day (8 miles). My average speed measured over several month is 21.5km/h. This includes riding through city traffic and stopping at traffic lights all the time.
Usually if the road is free my speed is around 25-30 km/h. I live in a pretty flat area and the elevation on my commute is not more than 60m (according to GPS).
Cycling the first week after my holidays was horrible - no stamina whatsoever and I was significantly slower.
Bottom line: Cycle as fast as you can, it looks like you are doing a good commuting pace already but listen to your body and slow down if you feel tired.
To loose weight you have to elevate your heart rate (elevate means not max. out) and a bit of muscle fatigue is maybe part of every serious exercise and is nothing bad at all.
I sometimes like to sprint between traffic lights just to mix up the exercise and to build more muscle from pushing harder. Some stretching after cycling can also do wonders.
The most important is that you enjoy it!