Help!!! I don't even know how it got in there. There is one bad spot and a few skid mark looking places around the inside of the dryer.

Hold a piece of ice against the "bad spot" then use the edge of an outdated credit card, or something like that to scrape away the now brittle gum. A citrus based product like "Goof Off" or "Citrisol" will remove the residue. Wipe down with rubbing alcohol the remove remaining residue from the cleaning fluid or just make the next load through the dryer a load of rags/cleaning cloths/old towels.