Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain in case if you have burnt the back of the mouth and the thing that dangles that is 
uvula causing Uvulitis, then it should have healed by now, but in case if it is persisting till now then it can be probably due to repeated injuries causing inflammation and gagging..
A common case for it can be 
Acid reflux while 
post nasal drip can also cause repeated infection, inflammation, swelling and gagging..
I would suggest you to consult an Otolaryngologist and get evaluated and a thorough clinical evaluation and investigations like 
endoscopy can be done if needed..
As of now do warm saline gargles, antiseptic mouthwash gargles, suck ice pops and avoid spicy and very hot and hard foods..
Hope this information helps..
Thanks AND Regards..