I put a thread on this subject on the Style and Beauty section a few days ago and there were lots of excellent suggestions for products and supplements. Take a look.
I think you're on the wrong forum, OP. Perhaps if you asked GNet HQ they'd move it for you. You'd get more responses then, because many posters tend to avoid News & Politics.
Mine's falling out at a rate of knots and the reason I know is that it clogs up the brushes in the hoover. It was so tightly wound round the brushes before I had to get the scissors to cut through it to release the hair. It must be dropping out as I'm moving around.
It can't be anything else but the medication, which cures one thing and causes another. It used to be so very thick as well.
My hair thinned following radiotherapy, then a diagnosis of under-active thyroid, then the menopause.
Treating it nutritionally has made a big difference. I have taken high strength Biotin tablets, also Gelatin powder, and Silica tablets. This has taken at least 18 months but I've seen a great improvement. PM me if you want more info.
If your hair is not greasy, could you try washing it less frequently? If you need to wet it to get it into shape, just wet it with water. This is what I do and sometimes I use dry shampoo instead. Obviously, you don't want to become unhygienic but perhaps washing your hair less will assist.
I realise that some people have a real problem with hair loss and I don't suggest that washing hair less frequently would help in that situation.
Washing less might just help someone with slightly thinning hair.