This is normal. He's curious about everything and this is a good thing. I suggest that you talk with him about blood and the circulatory system. Around that age, I gave my granddaughter an anatomy book written for children. We looked at it together. She looked at it by herself. In about a month she had moved on to something else.
Perhaps you've protected him from the site of blood? I suggest this because you said you wouldn't let him see the gash in his chin. It's best to let him see injuries and talk about what is happening or what has happened with him. This will satisfy some of his curiosity. I suggest the possibility that he's concerned about himself bleeding because he sensed that something was wrong when he was bleeding profusely and you wouldn't let him see it. The blood scares him because it's a part of the unknown and of course is associated with the pain of that event. He wants to know all about it. He's scared when he falls down. Not only because he fell but because he doesn't know that bleeding is OK. It's another part of life. He may be looking for an answer.
Also, I think, all kids are upset at minor boo boos. My grandson insists on a bandage for the tiniest scratch. Your son sounds typical to me. He just wants to know about his body and at the moment blood is his focus. I suggest you focus on blood, teaching him what it is and how it's a normal part of everyday life.