Normal participle clauses
German participle clauses work pretty much the same way as in English, which is not surprising since the two languages are closely related.
So the participle clauses you were not sure about can be easily translated into German participle clauses:
Besorgt über die Neuigkeiten rief sie das Spital an. (Worried by the news, she called ...
Here are some translations that are close to the original.
"Worried by the news, she called the hospital."
"(Von den Nachrichten) besorgt rief sie im Krankenhaus an." or "Besorgt (durch die Nachrichten) rief sie im Krankenhaus an."
Although, if somebody told her the news personally, you would probably leave out the parts in the ...
Better you don't try to copy grammatical features from one language to another. Better you try to learn to use a new language like native speakers. No German native speaker has English Grammar in their mind when they produce German sentences.
The two German sentences in your questions are correct, but unusual. German native speakers normally don't use such ...