Your body goes through a tremendous amount hormonally after childbirth. I always said it took a good twelve months after each of my kids to feel somewhat "normal" again.
Also, breastfeeding takes a huge toll on your body. All that work it's doing to produce milk.
Are you eating a good nutritionally balanced diet?
Did they test your iron levels, vitamin B12, zinc? Did they also test all your female hormones?
Remember that the state of your hair NOW is due to whatever your body was going through approximately three months ago, due to it's growth, shedding cycle. I bet that three months ago you were probably suffering from lack of sleep at the very least?
It can be frustrating trying to work out why hair thins but I'd say it's likely to be a combination of both hashi's and female hormones since they can so often be closely linked.
Are you able to take evening primrose oil while breastfeeding I wonder? It's supposed to be very beneficial for hair loss. But please check first.