Can I sue a business if I fell and broke my collarbone and it was someone elses fault?

Do you mean someone else other than the business? It depends on who "someone else" is. If "someone else" is an employee of the business, than you may be able to sue the business under agency law (the employee, in the eyes of the law, is acting as the business). If you mean "someone else" as in someone who has no stake in the business, you will probably only be able to sue that individual. I am assuming you fell on the business' property and that is where you feel you may have a claim against the business. If some action or lack of action on the part of the business or one of its employees (acting as employees) caused your injury, you may have a claim against them. If a third party intentionally injured you on the business' property, you may only have a claim against the business if the business reasonably should have foreseen that a violent act would occur on its property but failed to take steps to reduce the risk (e.g. if you broke your collarbone when you were being mugged and there is a history of such crimes on that property or in the vicinity).

You should consult an attorney (which I am not) for a full, professional review of your legal rights and potential claims.