I had period pain before and after kids but I wanted to acknowledge that the contraction thing is certainly something I find I feel with period pain specifically since having my kids. I find (and this is WAY TMI, sorry) that since having babies I am more prone to clots. Not every cycle, but most, I will have one episode of severe pain (usually on day 2 or 3) where I feel an intense "contraction"-type pain and this will result in loads of blood and a clot. Then it settles down for the rest of the cycle.
I think if you are worried it's never harmful to discuss with a doctor but that feeling sounds normal to me, personally.