Hallux refers to the great (big) toe

Valgus refers to the abnormal angle

Abducto refers to the angulation toward the second toe.

Common medical terms for bunion are Hallux Valgus and Hallux Abducto Valgus (HAV).
When your toenails grow thich and ugly

the above is wrong.

the answer is:: Hallux Valgus, also known as a bunion
Hallux valgus

(hallux = great/big toe; valgus = abnormally turned position of a part of bone structure)
hallux
Hallux valgus

(hallux = great/big toe; valgus = abnormally turned position of a part of bone structure)