IMO, it's quite clear in the police surveillance video that Zimmerman was free of bandages and looked surprisingly clean considering the struggle he claims to have been through (I personally did not find it as "grainy" as some people suggest).
If he had an open wound on his nose or the back of his head, the EMTs would have treated and bandaged those wounds. I seriously doubt that they would have let him leave with the open gash he claims to have had on the back of his head (especially if it possibly needed stitches) without at least putting on a bandage to protect it from dirt and possible infection. Yet I don't see that at all. I also don't see any of the lacerations and contusions that would be likely if his head had been smashed repeatedly into the concrete as he claims.
Additionally, in the video, the police officers are touching and handling him freely with no gloves on to guard against a possible biohazard - which they would (or should) not be doing if Zimmerman had any blood on his head and/or clothing. I find it very difficult to believe that they would be handling a man covered in bodily fluids without some kind of protection on their hands. That would suggest to me that not only was his shirt free of blood, but his jacket likely was clear of it as well.
The police report states that he had blood on his face and head, but doesn't clarify if the blood was his own, or Martin's - the two women who saw Zimmerman straddling Martin's body, Mary Cutcher and Selma Lamilla, stated that Zimmerman was pacing around the body, touching his own head and looking confused (this was during an interview with Anderson Cooper). So I'm not sure how clear it is that the blood came from himself, or from Martin.