I am rapidly approaching the same state. I'm 71. Steroid injections are a bit painful, but I have only had them in my wrist. They do work, however so I reckon that they are worth it.
It sounds as if your mum needs what I need i.e. new knees. I had my hips replaced in France and my surgeon told me (at the last one 2014) that knee replacements had come on tremendously and are now standard surgery. (He did them both and was working on ankles.) If I could afford it I would go back there and just ask him to get them done - but your mum and I are stuck with the NHS.
Anyway - go for the x-ray to get proper information and put up with the injection. The doctor will use a local anaesthetic, but as it wears off it will be sore for a couple of days - worth it if the result is pain-free movement for a good few weeks. I avoid tablets as much as possible and stick to paracetamol when forced to take a painkiller. If she can't walk unaided then she really needs swift action and needs to be more pushy.