What you are feeling is normal, the feelings of fatigue will lessen over time.
Part of what you are feeling is likely genuine fatigue from lack of fitness, while another part is likely your body playing tricks on you. The simple perception of effort has a lot to do with how much fatigue we feel (there is fairly new research demonstrating this). If you perceive a task to be difficult you will actually feel more fatigue than if you perceive a task as being easier (the task itself hasn't changed - nor your ability to complete the task). As you ride more, you will likely perceive the task as being easier (since you have successfully completed it) and for all intents and purposes it will now be easier even if your fitness hasn't changed. Luckily, over the same time your fitness will improve which will actually make the task easier. Now not only is the task feeling easier, but it is becoming easier too. Both combined will translate to further reductions in the perception of fatigue.
This is why there is truth in the colloquialism that it gets easier over time. Conversely if you feel that this is becoming an arduous task, your perception will actually increase your feelings of fatigue (again the task hasn't changed - nor has your ability to complete it). This is why taking actions such as improving how easily your bike rolls can help reduce the feelings of fatigue (the actually task hasn't changed much, but your perception of the task has changed, translating into lower a perception of fatigue).
The long and short of it is that 50 minutes twice a day is not a trivial amount of exercise, but is definitely manageable (assuming you are otherwise healthy). Personally, my commute takes about the same length of time (bit longer distance) and find it quite sustainable at 5 days a week. At 3/4 days a week I usually feel rested and ready to tear things up. Occasionally, I will feel days of fatigue but I find strangely enough I get re-energized by working through it (i.e., listen to your body and slowing down, but not giving up). I think this again plays back into the perceptions of fatigue vs true physical fatigue.
Again assuming you are healthy, perception may be a large component of what you feeling. If you are able to ride out the tough spot, it most likely will get easier. In two months time your perception may have totally changed. Rather than longing for a car, you will feel like a trapped animal whenever you find yourself stuck in one staring out at people riding by wondering why you didn't ride that day.