Her younger brother has become a millstone around her neck these days; he is bothering her with his debts which he’s made drinking and gambling.  (i.e. her younger brother who is a drinker and gambler is giving her a lot trouble asking her for a lot of money to clear his debts, and as a result she fells as if she were to carry a millstone which is naturally very very heavy)

There’s a bit confusion between the words ‘milestone’ and ‘millstone’: a ‘milestone’, which literally refers to a large stone placed by the side of a road to mark each mile/kilometre crossed on that road, is also used for an important event that is very important or an activity that a person does or a stage that a person reaches in their life, and a ‘millstone’, which literally means a large flat stone used to grind grain in mills, is also used to refer to a burden, problem or an obstacle that hinders the progress or joy of a person.