If you have not got the pH study of esophagus and manometry (pressure study) of food pipe; that would be recommended. If these investigations abnormal; that suggests surgery for the hiatal hernia and acid reflux would be beneficial. Laparoscopic Nissen fundoplication (this is minimal access surgery / called as key hole surgery) has good results in cases like you.
Some doctors would get the following set of investigations for the hiatal hernia / reflux laryngitis and your manifestations;
1) Barium esophagography
2) Ambulatory 24-hour pharyngoesophageal pH monitoring
3) A biopsy of the larynx which may show laryngitis.
Since you are not responding to the medications; Nissen fundoplication surgery may be needed. Following specialists are needed to work in tandem for treatment;
1) ENT specialist
3) Speech therapist, and
Following measures are helpful, meanwhile, surgery is planned (you may be doing many out of them):
1) Small 5-6 meals a day.
2) Last meal should be eaten 3 hours before lying down.
3) Avoid; fried or fatty foods, chocolate, peppermint, alcohol, coffee, carbonated beverages, citrus fruits or juices, tomato sauce, ketchup, mustard, vinegar.
4) Eat slowly so air is not swallowed.
5) Swallowing therapy by a speech-language pathologist.
6) Lose weight if obese or overweight.
7) Elevate the head of the bed by 6 inches.
8) Avoid tight clothing.
9) Stop smoking, if you do.
Please feel free for your follow up questions.
I would be happy to assist you further, if you need any more information.