Are there any free warrant searches for KY?

Your attorney got the matter resolved, but it still required you to pay certain fine amount. By failing to do so a warrant was issued for non compliance. Since it is traffic related it could result in the suspension of your license. If I were you, I would call the attorney who helped you. Chances are, if you get the fines paid, and whatever else is required, the judge will be happy. With this type of warrant, it is doubtful that they will actively search for you, but if you are stopped by an officer, and he finds the warrant, yes, you will be arrested..

Ask attorneys in KY, not here in CA. If the court told you there was a warrant, you certainly don't need to search for one. In general, to handle a warrant, you must turn yourself in to the issuing court, with or without an attorney. You'll try to negotiate a recall of the warrant[s] and negotiate a plea bargain on the Failure to Appear charge. You'll try to negotiate bail reduction or OR release. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. That can happen if you come in contact with law enforcement or customs anywhere in the US. On misdemeanors and infractions, your attorney can probably appear in court without the defendant being present.

You should pay the fine.

Pay the fine. It is not likely that your license will be suspended and any warrant for you will not be extraditable so you need not worry about that.

Get the fine paid immediately. That should take care of the warrant.

Call the jurisdiction where fine owed. See if you can pay it electronically or by mail. Ask if they will provide receipt and abstract. Also check if they will clear the warrant.