Justice of The Peace Warrant

What is the name of your state? Texas

I recently paid someone to do a search at the county level for warrants, it took 2 business days to get the results. This search came up clear. I am wanting to know if warrants issued by a Justice of the Peace (would be a class c misdemeanor) would show up in a check like this. About two years ago, I appeared before a justice of the peace set up a payment plan for issuance of a bad check and I did not follow through with the plan. I had also run the check to make sure that I did not have other warrants that I may have not been contacted about. I realize that I must pay the Justice of the Peace the fines for what I set the payment plan up for, but my main reason for checking was to make sure that I did not have anything else in a JP court or even worse something like a Class A or B misdemeanor for theft by check. Any help would be greatly appreciated.