B12 deficiency is certainly a possibility here, but there are a few things I'd like to add.
Firstly, disregard any name you find on a container of vitamin B supplements. Just make sure it says it contains "Vitamin B12". The reason for this is that B12 is not a single substance but rather a number of closely related substances, all of which demonsrate B12 activity.
Secondly, there's every chance a GP will think along the lines of B12 deficiency. However, in order to utilise B12 in the body, we need a substance called Intrinsic factor. Now intrinsic factor is made by cells in the stomach and lack of it is the usual cause of B12 deficiency in the western world. Lack of Intrinsic Factor can becaused by a number of intestinal diseases, stomach ulcers and duodenal ulcers. it can also be caused by recent lower abdominal surgery. If your mum has had any of these recently, then you may like to ask the GP if he can get her Intrinsic factor tested.
Thirdly, if your mum has recently had shortness of breath, diarrhoea, tiredness, dizziness, weight loss, tingling in the extremities, unexplained headaches or difficulty with balance when walking, these can also point to pernicious anaemia, which can itself be attributable to B12 deficiency along with the sore mouth and tongue. A simple blood test will reveal all.