My moms toe around the nail is swollen and it seems like her toenail is disintegrating?

Swelling around toe nail indicate Inflammation or Infection that need attention. The possibility of toenail disintegration besides suggesting Trauma also call Nutritional deficiency syndrome into question. In summary a visit to PCP is indicated soonest to avoid potential complications like Blood Infection (Sepsis) if trauma and infection have compromised the toe.