How can I find out what the status of a civil litigation case filed on my behalf

Here are just a few ways that may start you on your search:

If you know the attorney's name who represented you, ask the attorney.

Was it a class action or were you a minor at the time?
If you were a minor, you should ask your parent or guardian about the case location. If they won't provide it, you should start with the Clerk of the Circuit Court in the counties where you resided. Also, check the local papers. If it was a high profile case, you may be able to access it through Google.
As a last resort, you may hire a legal search firm or private detective agency that does background checks. The case should come up in the background check.