My toddler has this also (uvula stuck to a tonsil, no fever, funny voice/hot potato voice- google it, it's a medical term), and it's been this way for about 3 months after catching mono at a birthday party at Chuck E Cheese.
Our pediatrician sent us to an ENT who first prescribed a steroid to bring down swelling and antibiotics, as the tonsils on both sides are swollen. After the antibiotic course, the tonsils remained swollen with little change, so he has diagnosed that it's chronic tonsillitis and they will have to have be surgically removed soon.
If her tonsil seems enlarged, and she has "hot potato" voice (it sounds like she's talking with hot food in her mouth or like donald duck) you should definitely get her checked out soon. There is a suffocation and choking risk, and is something not to take lightly.
The ENT tells me tonsilitis is very painful, though my child doesn't act in pain. The ENT assured me that sometimes kids get used to it, or are too afraid to say something.