Part of the problem with a thyroid issue is that doctors tend to be a bit hesitant about giving a prescription for it. She needs to get a second opinion because if her thyroid reading is low, she needs a medication.
It's something I feel quite passionately about. I had tests for 12 years, and each time a different doctor said, "Oh, it's dropped a bit, but that's nothing to worry about". Dropping a bit isn't anything to worry about, but none of these doctors looked right back to the beginning to see that my thyroid reading had dropped continuously since the time they started testing me. By the time they did this, my reading was off the scale.
Is there another doctor in the practice she could go and see?
In the mean time, her hair will be very dry and coarse. She needs to use a really good quality moisturing shampoo and conditioner, and use a moisture treatment mask quite often. This will really help. Her skin and nails will also be dry and flaking so she could use a good quality cleaners and moisturiser and cuticle oil regularly to help with that.
There is nothing she can do to stop the hair loss (that I'm aware of), and colouring it shouldn't be a problem unless she goes overboard. In fact, you end up feeling so low - thyroid problems are often mistaken as a depresssion - that having her hair coloured and sorted out might make her feel a bit better.
The only other thing is that a shorter cut and learning how to do a proper blow dry to give her some volume might help?