Translation:Where is the hospital? I'm in trouble.
While that might be grammatically acceptable, generally we'd still use "the" even if not specifically indicating a particular hospital. I believe it's because "nearest" is implied in most situations, such as "Where is the [nearest] hospital?" etc. To use "a", it's more common to say "Where can I find/locate a hospital?"
困る refers to your emotional state being negatively aroused, ie, upset. It says nothing about what your situation is, whether you are in or out of trouble. If you watch Cops, you'll see dozens of people who are in big trouble but are cool as a cucumber. Not こまった at all. Bad translation, DL. Please change it immediately.