CanI do anything ifI feel that my public defender was incompetent?

Your right to counsel in a criminal case stems form the 6th Amendment to the Constitution of the United States.  The right to competent counsel is implicit therein.  If you feel that you were not properly represented then you have to file an appeal within the time constraints permitted in your state and request a new trial.  The best thing to do is to request a new attorney for an appeal and ask him or her to review the transcript of the trial court with an eye toward using the "inadequate counsel" issue in the appeal.  You will probaly need to hire someone yourself for this task, depending on what you were convicted of.  Get some recommendations. Good luck.

While you have a right to a fair trial, as well as the right to the assistance of counsel (which is the more relevant right) that's not the same thing as the right to a perfect defense. It may be the case that your attorney's advice and representation was so ineffective as to deprive you of your right to effective assistance of counsel. But if he "merely" did a below average job, that itself will probably not be enough--ineffective assistance of counsel generally needs to be very ineffective to provide grounds to overturn a verdict  or retry a case. You should try to speak to another attorney, such as from legal aid (or try local law schools; many run clinics to help people who don't have recourse to a good attorney) and see if it seems that in this case, the lawyering was so bad that you may have good grounds for an appeal.