I wonder what other English translations could make sense. The "official" one sounds fine. "Are my shirts small to you?" sounds odd to me. But the Turkish seems open to interpretation. (?) How about "Are my shirts too small for you?" or "Do you find my shirts (too) small?" The person spoken to is not necessarily trying your shirts on, are they?
Yes, I think the "you" here is trying my shirts on! I am asking if my size of shirt is small on/for your body.
The "in your opinion" meaning that @JenniferAb suggested is not what sana means here. If I wanted to ask whether you think my shirts are small on/for my body, I would have to ask for your opinion:
Sence gömleklerim küçük mü?
[But this is probably a place you should not use sana göre instead, because it means both "according to you" and "right for your purposes," and that wouldn't clarify anything.]
The full version of this phrase in Turkish is "Gömleklerim sana küçük mü geldi/geliyor?"
Since 'gelmek' requires a dative object, we use bana in this example.
• Ayakkabılar ayağıma tam geldi. → The shoes fit perfectly on my feet.
• Yüzük parmağıma bol geldi. → The ring is too big(wide/loose) for my finger.
• Pantolonumun paçaları bana dar geldi. → The cuffs of my trouser were too tight for me.
• Ailemiz büyüdü, bu ev artık bize küçük geliyor. → Our family has grown, this house is too small for us now.