Sorry to hear about that, and I am glad that you are more or less OK! Whenever you have a hard head injury
like this one you should definitely get in to see your doctor
to make sure everything is alright.
If you hit the front of your face or your nose on the diving board, then the nose bleeds could definitely be from this. You could have a broken nose, a laceration inside the nose, or a big bruise all contributing to the bleeding. If on the other hand, you hit your head on the side or back then this is much less likely to be the cause of your nose bleeds.
Regardless, head injuries are serious and should be taken seriously. There are multiple problems that can arise from hitting your head, including concussions of various severity. Your primary care doctor
will be able to perform a thorough neurological examination to make sure you are not suffering from any lasting damage from your blow to the head. Make sure to mention to your doctor if you are having headaches, dizziness, nausea, visual changes, trouble with memory or coordination, or any other concerning symptoms as these could be signs of concussion.