It probably is just anaemia. However if you're feeling breathless when resting you should see your GP as soon as possible especially if there is any pain but even if there isn't as they need to make sure you haven't got a blood clot. I'm sure you haven't but you should get checked out.
I was really breathless before I started taking my iron tablets for anaemia, but also I think you go through a stage where the baby isn't in "the fetal position" just yet where they have lots of room to move, and they take full advantage of it by shoving their legs up against your diaphragm. I have found that now he's run out of room slightly his legs are always down by my side and I'm a lot less breathless.
I got like this - going to an accupuncturist sorted it out - could be there lying on the couch unable to breathe properly and 20 mins later have no problem at all - and I'm sure it wasn't all in the mind.
Try carob for iron - put tsp of carob flour in breakfast cereal or in yoghurt, can also buy bars but not as concentrated. This got my iron levels back up amazingly fast with no side-effects.
but just as a warning I developed asthma in my last pregnancy (although you'd tell because it would keep you up at night) .. they told me it happened to 1 in 100 pregnant woman .. I had never heard about it before developing it, but like with all these things have now met a few people who also developed asthma