My 4 year old weighs 27lbs. Her tonsils are always swollen & she gags on food daily. She takes tiny bites & gets full quickly. How can we help her?

Take to ENT. She may have large adenoid glands and or frequent pharyngitis. She might benefit from tonsillectomy with adenoidectomy.
Tonsillectomy. If her tonsils are so swollen that they interfere with eating, then they are likely causing other problems too, like obstructive sleep apnea. The growth, development, behavior, and learning ability of a child is deeply effected by their ability to sleep properly. I urge you to see your pediatrician, then an ear/nose/throat doctor.