I see nothing wrong with any of your three sentences. All sound natural and essentially synonymous, though #3 to me sounds like the shame appeared later than the crying. No native speakers of my acquaintance would think twice about any difference in meaning between 'ashamed' and 'embarrassed', irrespective of how dictionaries might try to differentiate them.
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No1. Samantha was very embarrassed to be seen crying loudly in public.
No3. Samantha was very ashamed of being seen crying loudly in public.
Anonymous Is No3 a correct English sentence? Can No1 and No3 be used completely as the same me