It seems you've answered your own question, Vincent (assuming "a shop shop" is meant to say "a shoe shop").
"She went to a shoe shop."
Why don't we say "shoes shop"? Hmm. Well, "shoe" is an attributive noun. It modifies "shop". Attributive nouns are usually singular, regardless of how many of the objects are likely to be involved. For example, we say "car park", "bird tab