Sometimes things down there get a little mixed up when you are having your period. The organs in your pelvis sit in a specific way. From front to back are your bladder, your uterus, and your rectum. Since your uterus is sandwiched between your bladder and your rectum (the place where your poop waits until you are ready to go), when you get menstrual cramps the other two areas can get irritated. The uterus can bend a little forward and irritate the bladder or it can lay back a little and bug the rectum. It sounds like your uterus lays back a little and so when you get menstrual cramps the pain seems to be coming from your rectum and makes you feel like you have to go poop even when you don’t. Since menstrual cramps are caused by prostaglandins released by the uterus to help detach the lining, taking ibuprofen can often help decrease these cramps. When the uterine cramps quiet down, your rectum won’t be as irritated and you won’t feel like you have to poop. If your pain and sense of urgency to poop remains, even with ibuprofen, you should check it out with your healthcare provider.
I've never had that exact problem, but I know that gastrointestinal upsets aren't unusual during menstruation. Check Dr. Molly's answer for the medical scoop on it. As a first defense, I'd try managing it naturally and proactively. Before and during your period make sure you eat a healthful and balanced diet including plenty of fiber-rich foods (such as fruits, vegetables and whole grains) and drink plenty of water. Also be sure to exercise because movement creates (ahem) movement! If diet and exercise don't ease the issue, then bring it up with your healthcare provider.
Short answer? Yes. Long answer? Let's take a closer look at what could be aggravating the problem. Aside from period interference, constipation can also be caused by lack of fiber in your diet. Being a nutrition fanatic, I always recommend that people get their fiber from natural sources, like fruits, veggies, and whole grains. Try upping your fruit, veggie, and whole grain consumption the few days before and during your period to see if it helps. It's also important to drink plenty of water to keep everything moving. If those things don't help, and if the problem starts interfering with your life, it might be time to make an appointment with your healthcare professional. I have to say, I usually have the opposite problem when I'm on my period! So I understand how your period can interfere with your poop schedule in an annoying way. But making sure your nutrition is on point can really alleviate the problem!