There is no question posed but presumably you want to know if you have a case. The answer is maybe. If the store is found to have been negligent in maintaining the shelf, created the condition or had notice of it, then the answer is yes. You must consult with a personal injury attorney in your area who can investigate the matter and determine if the store was negligent. Get further treatment for your back. An insurance company or jury will not compensate for injuries that would have...
As indicated by Mr. Rubinov, you may have a potential products liability claim and should consult with an attorney as soon as possible. You should have your pre and post-accident medical records available for review as well as any proof that you actually consumed energy drinks in and about the time of your injury. Since you mention no time frame, the sooner you meet with qualified counsel, the better.
You're not obligated to accept the carrier's decision. You can "appeal" the decision in accordance with the policy or through the NYS Insurance Department or you can bring an action against the other driver. Not sure how much is at stake but you may want to speak to an attorney to get an objective look at the facts and your chances of success.
If this was a public school and you haven't filed a notice of claim, the answer may be nothing. If you haven't done so already, you need to consult with an attorney in your area and make sure your time to file hasn't expired. If you have an attorney and trust his/her ability, then he or she should really be answering this question. There are too many factors that need to be considered for someone on this site to venture a guess let alone give an opinion.
The posting does not state if your were injured. Assuming you were not, this is probably a question for a landlord/tenant attorney. If you were injured then you take pictures, get the medical treatment you need, report it to the buildings insurance carrier and go see a personal injury attorney in your area. That you agreed to use the service entrance by signing the lease does not mean you agreed to any negligence on the part of the landlord.