I can understand how hard it is to have heartburn. I am glad you are seeking treatment for it, and even went through a scope.
Finding H. pylori is routinely done in gastroscopy, and it may or may not contribute to your heartburn. Another purpose of the scope is to look for other problems which can lead to heartburn, such as a stomach cancer (leading to a gastric outlet obstruction), or a hiatal hernia. If your specialist did not inform you about these findings after he had done the scope, you probably did not have it, which is good news.
Eradication of H pylori may make your heartburn symptoms better, but you will need other lifestyle measures as well, such as quitting smoking, cutting down on coffee, tea, alcohol, spicy food, sour food and oily food.
Rarely, H pylori may not be eradicated with triple therapy. These difficult cases will require a different treatment regime for eradication. Your specialist usually will order a "Urease Breath Test" after you completed your 6 weeks of Triple Therapy, and a negative Breath Test will suggest complete eradication. If the Breath Test is still positive, he will step up to stronger medications.
TL:DR here are the important points
1. Complete your 6 weeks triple therapy and see your specialist for follow up
2. Changing your lifestyle is just as important.
3. Let your specialist know that your heartburn is still not better.
Cheers!