When I first switched to eating more plant-based, I was basically just eating salads for about two months because I really had no idea what I was doing and I started losing a lot of weight and my hair started falling out more than usual. I've since gained all my weight back and my hair stopped falling out more than normal by just doing two things, switching my diet to basing it more on fruits and starches and making sure I'm reaching my caloric needs.
I don't eat legumes and only eat very few nuts & seeds per week, so I really don't eat any high-protein plant foods. I just make sure I'm eating enough by the end of the day of what I'm eating.
Saying your hair was falling out too just makes me think you might not of been getting as many calories on average as you think you were getting. Were you using any calorie-counting app to help you calculate when on that diet?