A Frigid Bug

[DeathofaSaint]

A Frigid Bug (I actually think this title is really good! You should keep it)

I have convictions entombed in glaciation, (What kind of convictions? It isn't quite clear. What exactly are you showing conviction to?)
Yet springtime melts my frosted obstinacy. (You have an incredible use of vocabulary, it's really engaging and fun to read. This sort of hints at the springtime is when the cocoon comes out, you could expand that idea even further )
I weave a cocoon of icy expressions,  (Why exactly are you waving icy expressions? A single line explaining could be helpful)
shielding me from greater evils than Helios. (You have a really consistent use of punctuation which is very strong.)
Hidden behind silk and chrysalis,      (I like the comparisons, this whole poem is a very strong metaphor.)
I am a moth and a butterfly in the same very moment. (What is the difference between the two? A moth, in my opinion, is a duller butterfly.) 

Inside, I am the library of Alexandria, (inside what? A cocoon? Possibly end this line with a semicolon so the punctuation feels smooth) 
But alike, I am susceptible to flames. (That's an incredible simile.)
I rise from the ashes, not a phoenix,   (Did you mean "not AS a phoenix" that would be more clear)
But a burnt, misshapen bug bringing no more frigidity.  (really good closing word. I love the use of contrast in the poem. Cut out the word "more" for less redundancy)

(I'm also open to title ideas alongside feedback <3 )

For more big picture feedback, I think structure matters a lot here and you're doing a great job. You could try to make a balance between first sentence and second stanza. Having the same number of lines in each stanza (example, 6 in each two stanza) and there's a big swift between stanza 1-2, such as the first stanza is being in a cocoon, the second sentence is arises and coming out of the cocoon. You're clearly going for a "less is more" approach which I love, you could lean into that even further with balance between the two. 

But there's a lot you're doing really really well. I love your use of vocabulary and very strong images.  Great job!