The longer you wait the more difficult it will be for them to find evidence.
If you are planning on going to the police, you should go tomorrow. Tonight would be even better. The police have a procedure to follow. Most general doctors would not know what tests to run or what to check for other than a standard drug test. The police would need to start an investigation and check for evidence. The longer you wait the more likely evidence will be lost. They will probably need to search the rapist's apartment to look for DNA, drugs, or other evidence.
Unless he was very careful to remove all the evidence from the crime scene- there should still be evidence there to link him to what he has done.
Do you still have the clothes you were wearing when the event occurred? They may have DNA evidence so you should not wash them.
If you plan to report this, the sooner you get in the better. Sometimes waiting as much as 6 hours more might be enough for evidence to be removed/destroyed. Say, if he decides to clean house tomorrow and you waited til Monday. The sooner you get in the better.
Also, even if there is not enough evidence to convict- it will go on his file so if he ever repeats his actions again- it will be that much easier for him to be sent to jail.
FYI I would not tell your bf you are planning on going to the police. He could give his brother the head's up to destroy any possible evidence.