Did my attorney mishandle my suit?

If your lawyer started the lawsuit then he can't get out without a substitution by another lawyer or a court order.

You state that the "case was already submitted to the county". That might mean that the lawsuit has been started, and could be continued. As for the rest of the question, get your file back from your former lawyer (it belongs to you) and get it into the hands of another lawyer. If the malpractice case cannot be continued, you may have a malpractice case against your former lawyer. Unfortunately, malpractice cases are hard to prove, and you will have to prove that the lawyer committed malpractice and that you likely would have won the underlying case had he/she handled it properly.

I don't sue other lawyers but letting a case lapse beyond the SOL is malpractice.

If your attorney withdrew as counsel but, suit has been filed to protect the statute of limitations you simply need to hire a new attorney to pick up the case. This would have been provided to you by an order of the court and typically gives you 30 days to do so. If the attorney withdrew without protecting the statute, and the statute has expired, then you need to see a legal malpractice attorney to discuss your options.