I changed over to the injections, as the tablets had become a problem. Although I had had no experience of injections, and feared the whole thing, I found I can tolerate the MTX much better now (I still write off the day after, and plan an 'at home' day).
As to the hair loss, I was such it was happening. But, for me, it never became a big problem, and one day I relalised that I hadn't noticed any extra hair on the brush or in tht shower for ages, and so it must have been a short lived loss.
Take care off yourself