I'm feeling a small burning in the stomach all the time, and it hurts even more when I drink soda. The ER won't do anything. Should I be worried?

Stomach burn . this could mean you have gastritis (swelling of the lining of the stomach) or the beginnings of a stomach ulcer. Soda is very irritating to the lining of the stomach because if it's carbonation. I would recommend talking to a primary doctor about medication; things like omeprazol, Zantac, (ranitidine) Pepcid will help and are OTC remedies. If it gets more serious or persists then you may need an endoscopy.
A blood test. for H. Pylori might be your next step... this is a bacteria that can infect the stomach and cause gastritis and ulcers. If you have it, you need a 2 week course of antibiotics to clear it. And in the meantime, stop drinking soda!!