Based on the photo provided, it looks like your mother has an infection of a collection of hair follicles (medically known as carbuncle) or and infected cyst. I would strongly suggest that your mother visits a GP as soon as posible to get it assessed and get a course of antibiotics.
If the clinical examination suggests that there is a collection of pus (medically known as an abscess) under the skin, it needs to be drained surgically. At this size/extent, this can likely be performed under local anaesthesia by a surgeon (ENT Surgeon, general surgeon or a surgeon with training in the head & neck region).
Although you mentioned that your mother has this for 2 years, it is likely that it has been fluctuating in size and appearance as cysts and infected hair follicles can flare up from time to time. During a flare up, there is usually pain and increased swelling. If your mother has been experiencing recurrent infections, it may be better to have the cyst/infected follicles removed.
Hope this helps and all the best!
