。
I have a drug allergy.
Literal
Drug-allergy [subj-が] exist-[polite-ます].
薬アレルギー is a N+N compound noun — a common Japanese pattern for creating specific disease/condition names without a particle. Compare 花粉アレルギー ('pollen allergy'), 食物アレルギー ('food allergy'). Slightly more clinical and headlinish than the longer 薬にアレルギーがあります version with explicit に-marking.