Sorry to hear of your difficulties, but welcome to the forum. There are a lot of folks here in different stages of diagnosis and management, and many threads you should find helpful.
It's not uncommon for one type of PPI to lose effectiveness. Many patients find that some don't work well at all, but another type will control symptoms much better. Be sure to bring this to your doctor's attention, and he can write you another prescription.
I'm surprised that you were told to take the omeprazole only four weeks? (Also, you don't need a prescription for omeprazole, so no need to stop taking it if you run out. Just go to CVS, Walgreens, or WalMart.) Most PPIs reach full effectiveness in 3-4 days. The unknown here is the condition inside your esophagus/throat. If you have erosions and/or sore spots, they can take a while to heal over. But two weeks should be long enough for you to feel much better. Again, check with your doctor about another prescription.
If you've been diagnosed with GERD, your doctor should have explained to you that your condition requires daily management. On again, off again medication will only make you suffer more.