A dog's mouth may be swollen due to mosquito bites, allergies, injuries, etc. It is best to send the dog to a pet hospital for examination and treatment. If your dog is found to be injured, you need to clean the wound immediately, and then use ice cubes to apply cold compresses to reduce swelling. In serious cases, you need to send your dog to the hospital. It is usually best not to take your dog to places with many mosquitoes to prevent bacterial and fungal infections.