I don't know how long your case has actually been pending. After motions and discovery have been completed, cases are always calendared "for trial" but they take a long time for that to happen. Most times on the trial date, the case will get adjourned.
If it's truly your trial date in 20 days, the judge will likely not allow you to either represent yourself or to ask for a new public defender. Last minute requests like that after the case has been pending for a long while are generally seen by judges as delaying tactics on the part of the defendant. They will make your lawyer go forward.
If it's not really your trial date, I have not changed my opinion from what I said before. If you win this case, you have a brutality suit against the police. And you can also complain about their treatment of you now, for that matter, to Internal Affairs and to your state attorney general's office alleging brutality. But that is just one more reason that I'd urge you to leave your defense to a pro, because if you come out guilty of either of these charges, that's out the window.
This case is going to come down entirely to credibility. Don't blow yours by taking on more than you can chew. With something like this, a lawyer can be neutral. You're clearly angry and you have a right to be, but the angrier you appear in court, the more likely it will look to the trier of the facts like you were capable of assaulting the officers.
Tell the judge your lawyer does not return your calls, talk to you about your case, or contact your witnesses and you do not believe he is working on your behalf. Ask for the appointment of a new lawyer.
Without seeing the court papers, looking over the discovery, doing an investigation
, and conferring with the prosecuting attorney it would be professionally irresponsible for any Expert here to tell you what you needed to do to make out your defense. But if I haven't convinced you to stay with a lawyer, I'll be happy to opt out at your request so that you can get a second opinion.