If you did not get relief in your direct appeal or in your post-conviction petition you may have trouble establishing a civil claim. But by all means, consult an attorney who handles legal malpractice or civil rights litigation for a careful evaluation of your case. Maybe you have something to work with.
Unfortunately, if you have unsuccessfully gone through the appeal process, there probably is very little you can do on the civil side. When you initially pled, you informed the court that no one had coerced or forced you to plead. Now you claim to have been bamboozled and/or coerced but that will be very difficult, if not impossible, it to prove.
If you feel strongly about your case, you should consult with a seasoned attorney who will be able to assess the strength of your case and advise you accordingly.
Aside from the questions the judge would have asked you before accepting your guilty plea to determine that it was being made freely and voluntarily, you would have had to have consented in writing to be represented by a senior law student practicing under IL Supreme Court Rule 711. This form should have been gone over with you and signed in the presence of a supervising attorney. And chances are the judge would also have asked if you did in fact agree to being represented by a law student working under the supervision of a licensed attorney. It won't matter if there was a different public defender than "your" public defender supervising the law student as long as the student was supervised by some attorney from that office. In any event, even if successful in a civil suit, that will do nothing to "clear your name."
This answer is provided for informational purposes only and does not create an attorney-client relationship. Follow-up with a licensed attorney who regularly practices in this field is strongly recommended.