Welcome to Healing Well! I understand why your doctors immediately diagnosed Silent GERD. A "lump in throat" sensation is a common symptom. I'm sure you've searched the internet thoroughly, but here's a site that discusses the problem:www.everydayhealth.com/gerd/understanding-silent-gerd.aspx
Doctors often diagnose a problem based on symptoms alone. Your experience is very typical, so the best route is to treat it conservatively (a small amount of Priilosec--20mg once a day) and see how it responds, before going to the next level (for example 20mg twice a day, or 40mg once or twice a day).
I'm sure once concern you have is cancer. Here, the doctor is very correct. It takes years and years and years of untreated reflux to end up with esophageal cancer. Most if not all of people here who have Barretts, a pre-cancerous condition that can lead to cancer, have it without symptoms.
How long will you suffer from this? That depends. The cause could be a one-time issue that will resolve with just a couple weeks of treatment, or it's a condition that will persist. Silent GERD/LPR by definition could be suffered without knowing it. You could have had it without knowing, or you could have eaten too much, or have overdone drinking, which set you up for the symptoms, and they will resolve without trouble.
I think your doctor's orders sound sensible. Give yourself time to heal on the lowest dose. If after the weeks pass you don't feel better, let your doctor know, and he/she will likely increase your dosage to twice a day.
Keep in mind that this type of tissue takes a long time to heal, so you need to be patient.
Glad you've joined us! I'm sure others will be by to share their experiences.