My mom gets premenstrual syndrome, so am I likely to get it later?

Yes. Risk factors: high caffeine intake, stress may precipitate condition, increasing age, history of depression, family history, dietary factors (low levels of certain vitamins and minerals, particularly magnesium, manganese, and vitamin e) and also vitamin d.
Maybe. I don't know of any conclusive evidence of a genetic component, but it does run in families. The behavioral component to PMS could also be partially learned by example (i.e. You may act the same way as your mother did), but the physical symptoms are hormonally based.