This is actually VERY common during a panic attack. Feeling like you have a dry mouth/swollen tongue/can't breathe/can't swallow, etc. It happens to almost all of us during moments of panic or high anxiety.
The thing to remember is .. YOU'RE OK. Your brain is firing wacky signals that you're NOT ok, but YOU have to fight back. Get away to a quiet place (bathroom, closet, backyard, anywhere!) and close your eyes and FORCE yourself to breath slowly in and out. Count slowly to ten (or as high as you can) with each inhale, and then exhale slowly. This takes more control and concentration than you might think, cause your panic will make your body want to pant and breathe quickly. It helps me if I breathe with my mouth open, because that also reaffirms that I CAN breathe just fine, nothing's choking me, etc. I also say out loud, something like "I'm ok, there's nothing wrong" over and over until I calm down. Words are very powerful, just like thoughts.