There is no time limit on when a victim can call the police to report a crime. However, there are restrictions on when accusations can be made and a case can be brought to court in many places.
You cannot be charged for the upfront costs of a forensic sexual assault investigation. The way each state interprets this law can vary. Since 2009, states have been required to provide sexual assault forensic exams for free or at a discounted cost, regardless of their desire to cooperate with law enforcement. Starting in 2015, medical facilities will no longer be permitted to charge patients for examinations up front and then request reimbursement through their insurance after the fact.
Just because you gave someone your consent in the past doesn't mean they may continue to act in accordance with it. They broke the law if you didn't grant them permission, and you can report them for it. No matter who committed it or why, sexual assault is against the law.