The "expert" you got him from sounds more like a backyard breeder to me. Any reputable breeder would be offering to help you and wouldn't have sold him to you like that. It sounds like he could have a bacterial or fungal skin infection. Both of these things need to be treated by a vet, there are no home remedies for them. Oil is just going to make it worse.
As already said if your mom isn't going to be willing to take him to the vet then you need to find him a new home. Pets require vet care. He isn't going to get better if he doesn't get treated by a vet.