Yes, an indefinite article can be routinely used to precede an adjective that premodifies an uncountable noun denoting an emotion or state, as in the example you presented: ‚ÄúThere‚Äôs a terrible sadness in her eyes.‚ÄĚ Below are five more examples of that usage involving uncountable nouns denoting an emotion, condition, or state:
‚ÄúThere‚Äôs a certain magic in the way she sings.‚ÄĚ
‚ÄúAn enigmatic joy appeared on her face.‚ÄĚ
‚ÄúShe always feigned a forceful laugh that irritated everyone.‚ÄĚ
‚ÄúHe displayed such an open admiration that bordered on obsequiousness.‚ÄĚ
‚ÄúI could sense a brutal coldness in the way he looked at me.‚ÄĚ
This usage, though, doesn‚Äôt generally apply to all uncountable nouns. In particular, it doesn‚Äôt apply to an uncountable noun that‚Äôs grammatically singular but notionally plural like ‚Äúnews‚ÄĚ; indeed, this is the reason why this sentence construction you presented doesn‚Äôt work: ‚ÄúI have an amazing news for you.‚ÄĚ Instead, we say ‚ÄúI have amazing news for you,‚ÄĚ and, if more than just one news item are involved, we say ‚ÄúI have two amazing bits of news for you.‚ÄĚ Or ‚ÄúI have some amazing news for you.‚ÄĚ In the case of ‚Äújewelry,‚ÄĚ it‚Äôs also an uncountable noun that‚Äôs grammatically singular but notionally plural, so we can‚Äôt say ‚ÄúI‚Äôll show you a very beautiful jewelry.‚ÄĚ Instead, we say ‚ÄúI‚Äôll show you a very beautiful jewelry collection‚ÄĚ or ‚Äú‚ÄúI‚Äôll show you five pieces of very beautiful jewelry.‚ÄĚ For uncountable nouns, the modes of modification will vary depending on the nature and particular attributes of the particular noun, and it‚Äôs not advisable to generalize on that mode of modification until the particular uncountable noun comes up for use in a sentence.
The uncountable nouns you cited from a previous Forum posting of mine are as follows: ‚Äúdepth,‚ÄĚ ‚Äúemphasis,‚ÄĚ and ‚Äúsensitivity.‚ÄĚ ‚ÄúDepth,‚ÄĚ a noun denoting state, can be grammatically and notionally singular, as in my use of it in the phrase ‚Äúa false depth to what is being said.‚ÄĚ However, it can also be used as a countable noun that‚Äôs notionally plural, as in this sentence using ‚Äúdepth‚ÄĚ as a generic measure: ‚ÄúFor technical reasons, this device won‚Äôt work at depths of 60 feet and 100 feet.‚ÄĚ ‚ÄúEmphasis,‚ÄĚ of course, is an abstract noun that‚Äôs singular both grammatically and notionally, so it can be modified with an adjective preceded by an indefinite pronoun as in that usage of mine, ‚Äúa false emphasis to what is being said.‚ÄĚ As to ‚Äúsensitivity,‚ÄĚ it‚Äôs another uncountable noun denoting state, so it can modified the way I did in that posting of mine: ‚Äúa strong sensitivity to the repetition that often hides so well in such phrases.‚ÄĚ
I hope this explanation has further heightened your understanding of how the various kinds of uncountable nouns can be modified properly.