The hoarseness can be a sign of reflux. Most of us think of heartburn as the "real" symptom. I had frequent hoarseness for years before I started taking medication for my reflux.

But, your question about whether or not you need it is a good one. Did your symptom improve with the omeprazole? Was your doctor's plan for you to take it long term or short term? There are long term side effects such as limited magnesium absorption and bone loss that need to be considered if you are to be on it long term. 

Perhaps you could be treated with a lower level medication such as an H2 blocker rather than a Proton pump inhibitor. But, in my case after a few years of trying to take H2 blockers instead of PPIs, I wound up back on PPIs and will need to have my bones monitored. It's all about finding the balance between your diet, your stomach and your medication.

You may also want to discuss this with your primary care doctor who may be more likely to know about the long term risks. The doctor who did the thyroid surgery may have simply wanted quick healing of the esophagus after the surgery and long term follow-up will need to occur through your primary or through GI if necessary.

Best of Luck - Stephanie