What is my Mother experiencing? Hallucination, delusion, Alzheimer's and which doctor do I consult?

Hi My mother is 82. Of late she has been seeing and hearing children, guests who are not around. So far so good. But of late she is accusing my teenage son of slipping out at night to see a girl...!!!!.My son is at his wits and so am I. I am worried it is giving wrong ideas to the children. She wakes me up at night to tell this. I did show him sleeping in his room a couple of times, but next day morning it is the same. I am worried I too may start doubting my children.Which doctor (psychiatrist/neurologist/general physician) do I consult.I feel sad for her and do understand. But sometimes it gets a bit toooooo much, managing both. Pl. help.