Can I fire my court appointed attorney before my jury trial on a misdemeaner case?
Yes, you can. A court appointed attorney is not a requirement. Although, since you are facing a criminal charge you should have legal representation. especially since you are facing trial. If you want to now hire a private counsel you can do so. If you want another PD appointed to your case you may be able to do that as well; getting one is not automatic however.
In order to get a new court-appointed lawyer, you will need to request a hearing for substitution of counsel. That means that you can get a different public defender to represent you so long as you can convince a judge that this is necessary in order for you to put forth a competent defense. To seek such a hearing, you should write a letter to the judge that is presiding over your case, requesting a meeting with them and why. A copy of your letter should be sent to both the lawyer that you want removed and the prosecutor. Make sure both copies and the original (which goes to the judge) are sent certified mail, return receipt requested; you also need to keep a copy for yourself. Be sure to need list all problems that you are having with your attorney. Keep the letter short and to the point. And be sure that it is truthful; you do not want to jeopardize your position before the judge by stretching the truth or making false claims.
Additionally, you can contact legal aid and see if they would take you case. If not, check to see if there is a law school nearby to where you live; they typically run free/low cost clinics that handle these type cases. Also, contact the local Bar Association in your county; they may have a list of attorneys who will take your case "pro bono" (for free) or at least for a reduced fee based on your income/circumstances.
Note: timing is crucial. Whatever you do, do it immediately.