There are a few words with "-а" ending that can be used either as female or male nouns. There is even a special term for them. "Крошка" is one of that nouns. Nevertheless, male adjectives with these nouns do sound weird. "Мой крошка" or "крошка пришел/спросил" sound good. "Сладкий крошка"... I don't know.

"Врач" is a male noun. Although phrases like "хорошая врач посоветовала" are common in an informal language, you should avoid them in a formal text.