witt,
The spacing helps a bit. Let me show you what I mean.
Mother lies dying in the next room (This reads like a complete sentence. A period should be placed after "room.")
Memory-shadows cast by the moon (This reads like a compound subject. Well and good.)
Reveal the hidden sins (This reads like the verb and predicate that go with L1. There should be a period after "sins.")
My life had always been (This reads like the beginning of a new sentence. The option that it is connected to S2 is there, though, because it is not distanced from S2 by any punctuation mark. To me, it looks like the beginning of a sentence that continues through what is now S2, L1-3. If that is true, then the line break should be after "sins." And this line should be moved down to join the three circumstantial predicates that follow it.)
Pearls and thornless roses (This reads like a continuation of, "My life had always been." If it is, and if the two lines that follow also are circumstantial predicates, then there should be a comma after "pedestaled," and a period after "bubbles."
Protected and pedestaled
Drowned in champagne bubbles
Even though I am This reads like a circumstantial clause beginning a sentence in combination with the next two lines.)
Draped in diamonds (If my evaluation of the preceding line is accurate, then there should be a comma after "diamonds.")
My flesh feels cold as snowflakes. (As indicated by the period, this is the end of the sentence. )
Mother lies dying in the next room (As its twin above, this sets the state for your ruminations. If meant to be a lead sentence, there should be a period after "room.")
My soul is a frigid sapphire (This is a simple sentence. There should be a period after "sapphire."
What good did money do me? (If you felt it was important to use punctuation here, even though you led with an interrogative, then it should be just as important to use punctuation everywhere. In for a penny, in for a pound.)
My arms long for summer heat (Again, a simple sentence should end with a period. My only issue with this line is that it sounds like a longing for the healing process and that is theme of the next stanza. If it is and belongs there, I'd move it down to precede, "I need to feel.")
I need to feel (This is another simple sentence and a period would indicate that. If that was your intent, place a period after "feel." However, if this is a lead in to, "Arouse some sympathy," that is, that arousing some sympathy is what you need to do to "feel," then a comma should be placed after, "feel," and a period needs to be placed after "sympathy."
Arouse some sympathy This line could be circumstantial to L1 or indicative of how sympathy is to be aroused, that is, by being washed in brine. Which is it? If associated with L1, see the comment above. If to be associated with L3, then a semi-colon indicates that relationship. The other option is that it is the beginning of a list of three ways that could make you feel again. If so, then a semicolon after feel and commas after item one and two, and a period after item three.
Wash me in your brine (If, again, associated with how to arouse sympathy, then see above comment. If meant as a stand alone imperitive, then a period should follow 'brine." If associated with L2, then a comma after "brine.")
Rinse me in your blood (See above comment. If stand alone, a period. If associated with the preceding, still a period should follow "blood."
I yearn for sunshine (The last two lines are clearly a separate issue from what preceded. If you are going to use line breaks to indicate a new thought, then break after, "blood.")
And passion's poverty.
Line breaks could serve the purpose, if it were not possible for a given phrase to be associated with a preceding or subsequent phrase, and in that association confuse the reader or inaccurately communicate what it is your are trying to state. Appropriate punctuation leaves no doubt, and, contrary to trendy opinions, does not negatively impact on the flow or pace. That is more a matter of rhythm, of meter. That is a whole different topic.
Keep writing.
Bill