Yes, iron can cause constipation. Agree with some recent posters about getting iron from food vs a supplement. Red meats and liver are your best sources. Avoid taking calcium/drinking milk when having high iron foods. Eat high iron foods with foods high in Vitamin C as the Vitamin C helps the absorption of iron.
Read "Fiber Menace", the website or his book:
http://www.fibermenace.com/. Author recommends the direct opposite of everything we always hear. He recommends less water and to greatly reduce your fiber intake. His book states that fiber is a temporary laxative that bulks up your stool then your colon becomes dependent upon it for having a bowel movement, so you need more and more fiber increasing the size of your intestines and increasing the size of your stool. Or something like that.
Take Vitamin C to bowel tolerance to help you go if you are stopped up. Use a glycerin laxative if you can't get it out. Don't dig it out! Or take Milk of Magnesia, just don't do that long term as your remedy.
Take a good probiotic or eat lacto-fermented foods to help increase good gut bacteria.
FYI - was clogging toilets when pregnant too. Working on trying to resolve BM's via nutrition and things are definitely improving.