It's possible that some of your hair loss is not thyroid-related. When you're pregnant, you don't lose all the hair you normally would--it just stops falling out every day like usual. After the baby is born and your hormones settle down, you lose all of that. It's hair you would have lost if you weren't pregnant, so it's not extra hair, but it still looks like a ton of it. Around 4 months after both of my kids were born, mine came out like crazy. That is normal.
Since you also have a thyroid problem, it's probably worse than usual post-partum hair loss. I have heard that the rogaine shampoos and treatments are the way to go.