The responsibility is yours. Check with the court to see if the matter has been set. If not, contact the clerk or the court coordinator, depending on how the court works, to get a setting. If you don't know who is responsible for setting the case, call the clerk of the particular court and ask. When the case is set for hearing, prepare and file a Notice of Setting sending a copy to the other party by certified mail RRR or by fax. Put a certificate of service on the notice.
Per the Texas Rules of Civil Procedure, you must notify and copy the opposing counsel of any and all correspondence you have with the court including the filing of pleadings and setting of hearings. You also need to set the hearing yourself with the District Court Coordinator.
This is general legal advice. An attorney-client relationship has not been formed. Please contact an attorney for specific advice on your case.