The statute of limitations for forgery is ten years. CCP 12.01 (2)(C). Note that statutes of limitations is how long the State has to file the charges. Once charges are filed the warrant can be pending for a lifetime. The statute of limitations is also tolled if the fugitive leaves the state.
To check on a warrant you may be able to call the police agency that referred the charges to the DA's office but I seriously doubt they will answer the question. I can almost guarantee you that the District Attorney's office will not provide that information. Both entities will refer you to the warrant division of the Sheriff's Office, so you might as well just go straight to them since that is the office in Texas that issues warrants.