Learn Russian: Твоя щека грязная.

Because щека (cheek) is feminine, you must use the feminine form for both: обе. After обе, the noun takes the genitive singular form, which is щеки́. However, the adjectives go into the plural! So the sentence becomes: Обе твои щеки́ грязные.

Wait, in the phrase Обе твои щеки́ грязные, why are the adjectives plural if the noun is singular?

That is a classic tricky rule! When a noun is forced into the genitive singular by a number (2, 3, 4) or a quantifier like оба/обе, the adjectives that modify it take a plural form. For feminine nouns, adjectives take the nominative plural, which is why we use твои and грязные.

Does the stress change on the word щека when it changes form?

Yes, dramatically! The nominative singular is щека́ (stress on the end). But in the nominative plural (cheeks), the stress jumps to the first syllable and the е becomes a ё: щёки. Note that the genitive singular used after обе keeps the stress on the end: обе щеки́.

Could I use the short form of the adjective here and say Твоя щека грязна?

Grammatically yes, but it would sound overly poetic or dramatic for this situation. In everyday conversation, Russians strongly prefer the full adjective form (грязная) when pointing out a simple physical fact like a dirty cheek.