Civil lawsuits are filed in either state or federal court. State courts are usually allocated by county (and in New York City, by boroughs). For federal cases, go visit the Clerk of the United States District Court in Houston and ask for assistance. Tell them that you wish to search the current docket for any and all lawsuits filed against you. You would be the defendant. The clerk's office should have public computer terminals to have you examine the docket for your name.
For state court cases, go find the office of the clerk of the court in your county. Here too ask for assistance and say that you want to search the court docket for suits filed against you, giving your name. Again, you would be the defendant. To the extent your jurisdiction has electronic record-keeping, this information should be easily accessible via on site computer terminals. If your jurisdiction is old-fashioned and paper only, there may not be an easy method to search lawsuits by name of the defendant.
You may want to do this in the districts or counties in which you both work and reside. Beyond that, there is no easy way to determine if a lawsuit has been filed against you in another jurisdiction. However, any lawsuit against you should be filed in the county or district in which you either work or reside (which is the case in Illinois).
Warning: if you have been sued in any court and you have not appeared in that court, there is a possibility that a judgment has been entered against you. Depending on the judgment creditor's position as to whether you have been evading court obligations or not, and a court finding to that extent, you may be subject to a warrant for your arrest for failure to appear in court. Being present in the courthouse would make you more likely to be subject to execution of that warrant. If you believe there is any risk of this, you may want to seek an attorney's assistance. An attorney can perform all of the preliminary investigation into this matter (i.e., determine whether you have been sued in local jurisdictions, etc.) without exposing you to a risk of arrest for non-compliance with a civil court order.