I had and have bad constipation when I'm pg. I agree you probably need more fibre and to keep up the water intake. I take metamucil every day and I'm really aware of my fruit and vege intake and eating whole grain bread/cerial.
When I was in labour with DD, the nurse asked me how long it had been since I'd pood- it had been at least a day or two, so she gave me an enima...it was absolutely disgusting, but it worked! And it also helped bub move down a bit.
And yep it is the same sort of sensation to pushing bub out