Could the metallic taste in my mouth and burning feeling in my throat be caused by acid reflux?

Perhaps. Could also be caused from other medications. Galvanic reactions from dental restorations. Best to see an internist and dentist (if new dental work performed).
ABSOLUTELY. The mouth and throat have a standard ph of 7.2 to 7.4 (slightly alkaline). The highly acidic stomach contents regurgitated into the mouth and throat can cause a gastric acid burns and dissolve your teeth. Patients with gerd (reflux) and normal salivary function will have a reflex "water brash", that is, a flood of saliva to neutralize the acid. This is described by many to be a "metallic" taste.