Do I need the comma before "not" in "X, not Y"? What about when they're quotes?

Question

Unable to find this from googling.

The trees seemed to be shouting "I'm dead!" not "I'm alive!"

The trees seemed to be shouting "I'm dead," not "I'm alive!"

Which one of these sentences is punctuated correctly, and where would I find such a rule anywhere?

Also,

She is cold, not hot.

She is cold not hot.

When do you use a comma before "not"?

Answer 1

In Chicago Style, no comma in #1

6.123 When to omit comma or period.
Neither a period (aside from an abbreviating period) nor a comma ever accompanies a question mark or an exclamation point. The latter two marks, being stronger, take precedence over the first two.

This guidance isn't without controversy, though in this particular example, it works out ok.

A comma in #2

According to COCA, ADJ , not ADJ (two adjectives, with a comma) is the form that's used — searching without the comma brings up essentially nothing. Example (quoted in Collins):

Dogs are good, not bad.
Times, Sunday Times (2007)

Answer 2

For quoted phrases within a statement, The American rule is to enclose those phrases in single quotation marks, not double, and then punctuate as needed.

The trees seemed to be shouting 'I'm dead!', not 'I'm alive!'.

If this were something a person said,

"The trees seemed to be shouting 'I'm dead!', not 'I'm alive!'."

and

She is cold, not hot.

Which is consistent in that there is a comma before the not. "This, not that."