I've been writing lyrics but I can't seem to ever put them to a melody. I can kind of force them into a chord progression, but the vocals seem to sound melodically drab and unimpressive. Here are some short lyrics that I wrote a couple nights ago. It's kind of about my social anxiety and trying to halt my natural instinct of retreating into my shell around strangers, especially women, especially especially pretty women. Haha.

Her cold winds are blowing down through the trees
The frost runs through my veins, it's what I need

The folly I seek under my instinct sheets tells me what I want to hear, I'm compromised

My petty gains, they melt near her flame
"If you still can't see I guess that I won't stay"

Her poison warmth leeches but it soothes my weary brain
I tell it that this time, I think I'm here to stay

I realize it's really barebones and doesn't really follow any structure...some feedback on it would be nice so I can know if it's worth modifying.
As I was saying, I know what chords are in each key and everything, I'm also really into making fingerstyle instrumentals and I extensively use alternate tunings, my style is in the vein of john fahey and leo kottke. I can jam on guitar all day and I hopefully my words at least make sense, but when I try to combine the two I come up with nothing. What do you guys think I should try/what do you guys do when you write songs? Words or music first? Same time? Any tips would be awesome, I really want to give this a legitimate shot.
We can't really tell you how to write songs, you've just gotta kinda sing along, play your songs and hum along a melody then put those words to the melody. If you struggle do both at once then record your guitar parts and sing over that.
All I want is for everyone to go to hell...
...It's the last place I was seen before I lost myself

Quote by DisarmGoliath
You can be the deputy llamma of the recordings forum!
I like your lyrics. However, sometimes when I find myself starting to write lyrics I find that it might better be suited as a poem instead. Don't force songs to form. It has to be natural because when music is forced, it's obvious.

The chords and emotion to back up your lyrics will come into place in your head one day. Sometimes it's hard to figure out what vocals to put over certain musical arrangements, and vice versa.

You're a good lyricist, so keep it up. The rest will come into place.