I don't know that I have experienced exactly what you have, but I can tell you that my bowel movements just before and during my period are.... yucky, and have been for as long as I can recall (I'm 40). I don't know how else to describe it without getting too graphic and gross. And, it is very common. Google "bowel movements during menstruation" and you'll see what I mean. A friend of mine calls it "period poop."
As to the infertility question, I think you're referring to symptoms of endometriosis, which flares up during menstruation and can cause painful bowel movements. If you've not been diagnosed with endometriosis, you are probably fine. However, if you have a concern about it, you should talk to your GYN.
Also - do you use hormonal birth control? I had to stop using hormonal birth control because it was causing me to have weird digestive symptoms that I wasn't willing to live with. That's something else you might want to talk with your doctor about.
If you don't mind me offering a little wisdom from this side of the hill... Keep in mind that as you get older, your body, your cycles, etc will go through changes. It's prudent to track your cycle, make note of changes and if anything seems drastic or really "off," talk to your doctor. But it's also important to remember that what is your menstrual "normal" now might not be the same 10 or 15 or 20 years from now. When I was younger I thought I would simply get my period every 28 days (with pauses for pregnancy) on and on until I hit menopause. I wish someone had told me that it was normal for our bodies to change over time. OK, old lady speech over. Take care!