I dont' think UTI's have anything to do with your period being late. Make sure you go to the doc if you think you have a UTI. Sometimes a burning sensation can be yeast. They can check your urine there.
Is there any possibility that you are pregnant? My sister had UTI's when she first conceived. Mostly she had pressure on her bladder from her uterus expanding, but she did get UTI's a few times in her first trimester.
The first thing that I did with my recent UTI was take a preg test, just to make sure it wasn't the same thing.
Sometimes stress will make your period late, or skip it altogether.