Sleep Study. Swelling of the uvula is commonly associated with mouth breathing and sleep apnea. You should be evaluated for sleep apnea especially if you have other risks such as obesity, daytime sleepiness, a family history of sleep apnea and a large neck (greater than 17 inches in men and 16 inches in women).
Tylenol/Sleep study. Temporary improvement in symptoms can be achieved with over the counter meds like tylenol (acetaminophen) and motrin. But in a bigger picture you probably have issues with sleep called "obstructive sleep apnea" and you need a sleep study to see if you need a cpap. A device which will help you breathe better and sleep better. See your dr. To avoid other several major complications.
Chew on ice. Chewing on ice can be helpful, taking antiinflammatory medication can help. It sounds like you need to see an ENT doctor for evaluation of your airway. I have operated on several patients with similar problems quite successfully.