Let's

[Todd]

Hi,

Welcome to the site! Yeah love poetry is hard to pull off well. It's easy to move into a sort of emotional shorthand that doesn't really have any emotive power. I'll give you a few comments in the lines and a overall suggestion to consider.

So beautiful that I can hardly breathe.--beautiful sounds like its saying something but its really quite abstract and vague. 
Your smile bright like the sun. I want to stare,
but can't. Your gaze piercing me like a scream,
reverberating through the air inside--This air part is a bit at odds with the content of your first line
my lungs, the blood within my veins, my soul.
I'm hot and cold at once, and so alive,
awake, because you're better than a dream.--Better than a dream doesn't really say much.
I want to cocoon myself in your hair,
and tangle up our fingers, legs, and arms.
To brush my toes against your toes, to feel
your lips against my lips. Let's fall in love.--Let's fall in love is shorthand for the experience that demonstrates it happening.
I promise it will be so wonderful.--weak abstract ending

Okay so I know your thinking, did you like anything? Possibly. There's an interesting approach that you're hinting at in places:

I can hardly breathe
Your smile bright like the sun. I want to stare,
our gaze piercing me like a scream

You flirt with the idea of love unmaking a person, robbing them of the ability to function. I want to talk but I can't get enough air, or my lungs collapse. I look at you and you burn out my retinas. When you look at me it is like a scream.

I'm not suggesting a rewrite there just drawing out what I see. This could be an interesting love poem if you developed an angle like that with less shorthand and more specifics. It may not be what you're looking for but figured I'd mention it.

Best,

Todd