To the person who posted above, thank you. I too have experienced this twinge-like occasional pain down on my left side. It first happened a few months ago at the start of my period.
I went to my doctor, who sent me for an ultrasound on Day 10 of my cycle. The ultrasound found a follicular cyst (and nothing else). On Day 16-18 of my cycle, I experienced a sharp, stitch-like pain as described here. It was bearable and not too bad, but worried me. After that, all pain went away.
I then had a pain-free cycle. Then, the next cycle, I again had the same twinge-like pain in one side beginning with my period. I don't know why the pain has started with my period both times, but it struck me that this is also what the previous poster wrote.
Finally, these two cycles have been shorter than usual by about 5-7 days, which is very unusual for me. My doctor has also been saying I could go on the pill and I will probably do this, because even if they are harmless, they worry me!