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Even if you were not breastfeeding it would be normal to have hairloss after a pregnancy. Basically what happens is when you are pregnant your body is producing all sorts of hormones, even growth hormone. This makes some women get very thick hair and some women even have their feet grow. Then after pregnancy the nice thick hair falls out because those hormone levels start dropping.
It really may not be related to your breastfeeding.
Keep on with your breastfeeding and in a few months your hair will stop falling out as much. Don't worry you won't lose all your hair.