Look, when you're the sole witness to your attack, and there's NO evidence of the attack, and the attacker is countering that you started it and he never touched you, so that your word is all that we have to go on....
DON'T start lying to the police about things that are provable. You will be discredited, and your case will be closed, under the heading "Unfounded."
Even if the Po-po want to believe you, they can't take something like that to a judge, and ask for a warrant. There is a "credible witness" standard.