in the future when it gets this cold its a good idea to let the water drip from your faucet even when youre not using it. it isnt a guarantee but it helps long enough to keep them from bursting due to freeze so they can thaw

as for your landlord. you can withhold rent until they come and fix the issue. if they want to take you to court then they wont have a case because theyre responsible for the property and it wasnt you who damaged it