You are entitled to nothing unless you can prove that the bursting pipe was because of the landlord's negligence. You would have to prove that the landlord was aware there was a problem and did nothing about it.
This came as a total surprise to you. Logic says it came as a total surprise to the landlord, too. If this had been your own property, your medical insurance, or you, yourself, would cover your injuries. It is no different when you rent, unless you can prove negligence on the part of the property owner.
Additionally, in a property owner's defense, if a good lawyer can argue that your injuries were not caused by the bursting pipe but by your own action/inaction, you would lose. Had YOU not made the decision to put yourself at risk by trying to shut off where the hot water was, and instead gone straight to the main shutoff, you would not have been injured. And even when you rent, it is incumbent upon you to know where shutoffs, circuit breakers and other safety features are located, so that in an emergency, you don't take extra time having to look for them. Even if negligence was proven, any award you got would be reduced by the percentage to which you contributed to your injury. If negligence was proven, you might be awarded full recovery for the depreciated value of your possessions that were destroyed by the leak, but you may get little or nothing for the injury, if it can be argued that you were injured only because of your own unsafe response to the leak.