You poor thing! I am currently 23 weeks and suffered with constipation for the first few weeks...but rest assured it does get better! It may well be the iron in your vitamins, but also progesterone slows down your digestion when you get pregnant, to make sure your body has time to absorb all of the nutrients from your food to help you grow the best possible little human. Which is great in theory, but can lead to you feeling horribly bunged up. It's such a magical time! 
As PP have said, prune juice is your friend - keep it in the fridge and it's a bit less vile. You can also have fybogel which you can get from the chemist - it's a high-fibre powder that you mix with water. Get the orange flavour, mix it with a smallish glass of water, stir it THOROUGHLY and drink it straight down while it's still swirling - then chase with half a pint of plain water. In my opinion it's even worse than prune juice, but it does work.
Also exercise if you're feeling up to it will help get things moving, and obviously lots of fruit, veg and fibre in your diet.
Finally, when you are trying to "go", try putting your feet up on a small stool (often a bathroom bin is the ideal height) so you're in more of a squatting position. This helps straighten out your gut and will help things move more smoothly. Also don't push if you can help it (but you probably know this from your previous experience) - I found "J-breathing" helpful, where you take a deep breath in and then breathe out through your nose and visualise the breath going all the way down into your tummy and out of your bum 
It's a hypnobirthing technique (so may be useful in a few months!) which helps to relax your muscles and keep everything "open".
God I sound like a poo guru. Pregnancy does funny things to you.
Good luck and congratulations on your pregnancy! 
