Your chances are very slim. You are asked when you plead if you are doing so freely and voluntarily and you must have answered "yes" for the plea to be accepted. The court will view an attempt at withdrawal as buyer's remorse and deny it.
I agree.. You didn't hire a public defender, I assume you requested one. If you were present for the plea the judge asked you a serious of questions about the plea. Nonetheless you can still attempt to withdraw your plea. Talk to an attorney and they will tell you about possible grounds to withdraw your plea and you may be granted. Good luck!
Generally speaking, I agree with the other attorneys that the chances are not good. One potential factor that is not clear is how long ago this happened. You may want to consider calling the public defender's office to see what they have to say. Good luck.