As Ms. Glenn said it depends on the attorney. The public defender's office is swamped with cases and are funded by the State. So, a private attorney typically has more time to give each case individual attention and has more resources available. However, there are excellent PDs out there. If you can afford to retain private counsel, you should do so, as the Public Defender's office is for people who absolutely can't afford a lawyer.
Was it a charge that was dropped? Has someone been using your identity? You will need to find out what happened so that you can address this issue with FDLE. You should contact a criminal defense attorney to assist you with this matter.
Your question is not completely clear. Is the person you don't want to testify against your co-defendant? Did the State give you immunity in exchange for your testimony against this co-defendant? If that is the situation and you do not testify, I am sure the State will not grant you immunity as you are in breach of your agreement with them. You should consult with an attorney before you do anything, as it sounds like the repercussions will be serious.