Hello Lucy,
Welcome from me too,I'm sorry to hear of you and your mums situation.
I have and still am going through this with my mum too,(she has been in hospital for a couple of weeks but is coming home next week.
Noorza is right,the doctors weigh up the risk of medication and they can only hope something suits or works for your mum,they may try a few different ones if the amitriptyline doesn't help.
My mum is on mirtazapine at present,which,so I have been told,has made her sleep better and less agitated,and she is now making an effort to eat a few mouthfuls of food now. I take amitriptyline myself for fibromyalgia-joint stiffness,it does help me,but I don't have dementia-yet..
It takes a few weeks for the medication to build up in the system usually,so I don't know if this is the same with Alzheimer's patients..
You might have to wait a while to see if any side effects-good effects appear..But I wish your mum well and hope you get some respite from these difficult days..
Jane