Any pain such as that is not normal and should be checked out. We do expect some grumbly aches and pain when starting this but not excruciating pain.
Lower back pain is not normal for new runners.... or anyone really... so..you have the correct shoes, warming up properly and you are taking it gently... then you have a choice;
Try some simple back exercises...here is a post I put out on the Strength and Flex forum ( a great place for exercise ideas),
Then when everything feels easier head out... slowly, try to land lightly ( we may hold ourselves tensely at first). kiss the ground with your feet and see how it feels. If all is well then make sure you do those post run stretches and carry on.
If the pain is still as bad as you say, after the run, then a Sports Physio' or your GP are your next port of call. Never run through pain or mask the pain with painkillers.
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