Harmonizing vs. "Melodizing"

So far, when I try to write I song, I start out with putting together a chord progression, and then I write a a number of melodies and variations on top of it. However, I’m not a professional musician or songwriter, and lately I’ve been suspecting that maybe I’m approaching this backwards.

Because I start with chords, a lot of the time, without noticing, I end up building in my mind a kind of fixed, silent melody with the perceived main motifs of the chords; my ears adapt to it, and then every melody I write on top is heavily influenced by that kind of perceived cadence and limits my imagination. From that point on, I end up perceiving every melody I come up with as either too bland or too out-of-place.

I’ve tried doing it the other way around (melody first, and then chords). I can make it work with shorter hooks and whatnot, but building longer, varied melodies without a chord progression already underneath feels awkward for me, and I don’t know if it’s because I’m used to doing it the other way around, or because I’m not supposed to.

[tl;dr]

Is there a “proper” order in writing a song when it comes to chords vs. melody?

I have that problem too, although I’m a musician myself. I have the chords, then I write some melodies, but it seems that there are only two choices: too complex melodies that don’t sound good (dissonant or chaotic) or at the other hand: very “heard-before” melodies… Another problem that I have: I can 't seem to make a song that’s longer than 1 minute… My inspiration runs dry…