。
I feel like my tonsils are swollen.
Literal
Tonsils [subject-が] be-swollen-[state-ている] feel [subject-が] exist-[explanatory-のです]-[but-が].
A hedged medical complaint. 扁桃腺 (へんとうせん) 'tonsils' — literally 'almond gland', reflecting the almond-shaped appearance. はれる ('to swell, become swollen') is the standard verb for swelling/inflammation. ~気がする ('feels like, has the sense that') is the tentative impression pattern. The ~のですが ending softens the statement into a 'I'm not sure, but...' hedge.