Have this strong compulsion to colour my hair red.

Alas, my hair has been falling out in clumps lately due to hormonal changes related to the thyroid. The upside is that hair will grow back once my hormone level regulate itself to normal but it's going to take a long time. And I didn't have a lot of hair to begin with. Meanwhile, the number of strands has thinned considerably. It's like hide and seek with my scalp now.

So I am staying far away from chemicals, cuts and combing. Any recommendations for hair growth supplements?