Hi Kate,
Sorry to hear about your Gran, she sounds a gem.
OK – several things I'd suggest trying. As Jonquil suggested, you could try persuading her to re-visit the GP?
A lot of the stronger, prescription only strength medicines can make you feel quite sick and dizzy, but her GP might prescribe a different type but equally effective pain relief to try and see how she goes.
On top of that, it might be worth asking the GP if your Nan could be referred to Physiotherapy and / or Occupational Therapy.
The Physio's would give her exercises which can often do a lot to help with arthritic conditions. The OT's would carry out an assessment at home and if necessary, provide any aids for her to use at which might help make things that bit easier (such as kettle tippers / dressing aids / grabbers etc)
Until you can arrange to do all this, I'd advise her to try using some heat therapy in the form of something like "Deep Heat" cream and wheat / heat packs. You can buy these in any pharmacy for a few quid.
They are very helpful in reducing inflammation and pain with things such as arthritis.
Glad to hear she has such a caring and supportive Granddaughter! Folk like you are few and far between.