Can I sue my lanlord?

It snowed a couple days ago, and my landlord had shoveled the sidewalks but forgot to do the stairs. I live on the second floor. Being 7 months pregnant I always hold on to the hand rails but even those were icy. Without warning, I slipped and fell down the stairs. I spent hours at the doctors office making sure my baby was okay. Doctor stated there was some distress but the baby is fine. I however am bruised everywhere. I can barely get out off bed. My partner had gone to the manager and told him what happened. The manager had assured us he would have the stairs de-iced but he has not. I have a doctor's appointment tomorrow and I'm terrified that it will happen again.