OP, as far as I'm aware, the MAP is the progesterone-only pill which is safe for breastfeeding. Even if it does have oestrogen too (combined pill) it's not actually going to do your baby any damage, it's just that oestrogen suppresses milk production, so you might see a bit of a drop in your milk supply for a day or two after you take it - but if you offer the breast lots, then it will come back quickly. But do speak to the pharmacist. And good luck
I don't know who gave you that information, Homestar...but it's not true. Lactational amenorrhoea is a very effective contraceptive method - better rates that condoms and similar to the pill. (around 0.5 - 0.6% 'failure' rate, ie about 1 pregnancy per 200 women). http://www.kellymom.com/bf/normal/fertility.html
In quite a big study in Pakistan, using the lactational amenorrhoea method, the rate of conception at 6 months (of exclusive breastfeeding) was 0.6%, and at 12 months (with gaps of no longer than 3 hours between feeds, I believe) it was 1.1%. (source: http://www.ncbi.nlm.nih.gov/pubmed/7672141 ).
That's not to say that it's not without problems, don't get me wrong - for a you can't judge when your first period is going to return and you become fertile roughly 2 weeks before that, and for a second you can't have a gap of more than 3 hours between breastfeeds (including overnight) for it breastfeeding to work as a contraceptive - but if you are doing that, it's a very effective contraceptive...at least until it's not
But you're not most fertile in the 6 months after you birth a baby. At least not if you're breastfeeding.