Hello
With the given symptoms your mother seems to be suffering from upper respiratory tract infection. Since most of the URTI are caused by viruses they only require symptomatic treatment like DOLO 650 and anti allergic cough syrup. However elderly are more prone for catching secondary bacterial infections and will require antibiotics.
Next Steps
If her condition seems to be worstening, she would require antibiotics for here sore throat. In the meanwhile you can start steam inhalation, warm saline gargles along with what you are already doing. Try to avoid her from getting cold exposure and keep her warm with plenty of liquids to drink. Hot chicken or veg soup will provide her with lot of comfort.