You're between a rock and a hard place. Either get the money to hire the attorney of your choice or work with your public defender the best you can. There are some excellent lawyers in the public defender's office and they are in court every day.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
I would not be so fatalistic about the public defender's office. There are some excellent attorneys there. Ask to meet with the person and spend just ten minutes going over the police report, preferably in an afternoon when they are not so frazzled with court. If, however, you are still disappointed with their focus or interest in your case, call a few big, big law firms and ask if they provide pro-bono criminal defense services. You might be pleasantly surprised.
The term specialist usually refers to an attorney who has received the title by completing certification as a "criminal law specialist" for example. While undoubtedly many of these attorneys are very invested in their field, and are probably good at what they do, you do not need a specialist. You need a good attorney who cares about their clients. This can come at a premium, but you run the risk in hiring a private attorney for cheap who doesn't help and you run the same risk with an expensive one. Make sure you meet with several and don't be influenced by grand promises or cheap prices. Look for someone who is realistic, but confident and has ideas of how to defend you.
If you are dead set against going with a public defender, figure out how to get the money together for an attorney you're more comfortable with. Your case sounds like it's potentially complicated. You are facing serious charges that could carry a lot of prison time depending on your background and the particulars of this case.
That being said, public defenders do a great job. I'd recommend you think twice before writing them off entirely. If you can't hire your own attorney and have an actual conflict with the public defender's office, the court can turn to other appointed attorneys to represent you.
THE ABOVE ANSWERS ARE NOT LEGAL ADVICE. They are intended for general information only. You should not rely on answers given by me or anyone else in this forum. True legal advice requires a complete and thorough review of facts, circumstances, and documents and many other elements. An explicit written agreement to form an attorney-client relationship and establish confidentiality is essential. These things cannot occur in this forum. Mr. Harper is licensed to practice law in California and his answers may not apply in this or any other state. There is no implied or actual attorney-client relationship arising from participation in the Avvo forum. You should speak with an attorney licensed in your state, to whom you have provided all the facts before you take steps that may impact your legal rights. Mr. Harper is under no obligation to answer any emails or phone calls related to this or any other matter.