Thank you for your question. Chest pain is always a very distressing symptom to have to deal with. In addition, it can be a sign of very serious health problems, so it is important to present yourself to an emergency department. First, you need to have heart blockages ruled out as these are the most serious cause of these symptoms. This means that you will need to undergo a stress test. Your symptoms do sound like they could be gastrointestinal in origin. If your symptoms did not response to the omeprazole, then you may need a higher dose or it might not be GERD. Chest pain with swallowing might be an esophageal problem such as esophageal spasm which can be very painful and occur at rest.
I would suggest that you present immediately to an emergency department. The reason for this is the chest pain can be very serious and I cannot tell from your question whether or not this is heart related or due to some type of gastrointestinal problem. You should do this if you having active chest pain. If you are not, then you can see your primary care physician
in the morning for a stress test. If this is normal, then referral to a gastroenterologist
to rule out reflux and esophageal spasm is the next best step.