#1
I'm always coming up with little melodies, or progressions, or some kind of idea

But I can never fit words to go with them, I can't really sing and play guitar at the same time yet, so playing a melody and trying to sing ideas on the spot never works. I'm also not a singer, so my voice doesn't sound good singing along ha

Whenever I try and hum a vocal line I find myself just following the chords or the changes too much, sounds very generic and unoriginal

Any tips?
#2
Have you ever written poetry? 

https://en.wikipedia.org/wiki/Metre_(poetry)

Look through that, try writing a few poems, and see if you can develop a sense of rhythm around the words. Once you do that, you can match the rhythm of the words to the rhythm of the melody.
#3
It seems you've got most of the components of songwriting but just can't connect things with each other.

These are some things that may help:

1) Either learn to sing or team up with a singer. I write the songs, sing them to my vocalist with my horrible voice, he gets the idea, then makes his own thing. Which is most of the time a little different from what I had in mind but equally good or even better.

2) Start training yourself to play and sing (you don't need to train your voice, you're writing songs not singing in public). It's actually easy if you take it step by step. Strum say, a G chord and sing something with a tune, whatever it is, whatever the words are. Just make sure you're in key, that the notes you sing sound good with the chord. Then do it with another chord. The harder you find it, the less chord changes you need to make. You can even strum one chord and sing along with it. It's still a good exercise.

3) Don't worry about being unoriginal. Just write a lot of songs, the best you can do, but not necessarily new ideas. New ideas will eventually come up on their own. I never sat down and specifically thought "I want to write something different". I write what I want to write and sometimes, it actually comes different from anything I heard on it's own.

4) Keep it simple. Some of the greatest hits have two chords.

5) Every songwriter has his own starting points, but in my case, I prefer coming up with a melody line and lyrics at the same time, or nearly. Words with a tune. Probably one or the other does come first but I don't consciously think about it. I just get a line in my head and sing it.

6) Keep a notebook on you and write songs any time you get inspired. Don't wait until you have a guitar on you. If a cool tune and melody line come in mind, memorize it or record it. The idea of one of the songs I'm most proud of, came on a bus stage. I had nothing to write on, record or anything. I memorized the tune and when I had access to the guitar, I found the chords for it.

7) Use power chords (especially if you're into Rock and Metal) to write songs. Eventually you would want to embellish your riffs with more than power chords, but power chords are very easy to sing along to, so that's a good way to get started.
#4
There's a reason why many of the best songwriters were parts of a team. Some famous songwriting teams were like Lennon and McCartney who each contributed music and lyrics. But most of the teams consisted of a composer who wrote the music and a lyricist who wrote the words. When I was in a band with a guy who was an outstanding song writer, he said putting a melody on top of words was much, much easier than putting words on top of a melody. The natural rhythm of the poetry was easier to put notes to than trying to make the syllables of the words match the meter of the music. 

So, I suggest that you either (1) find yourself a Bernie Taupin to write lyrics for you, or (2) work on writing the lyrics first, then fit a tune to the words. 

And understand that what I've recommended is mostly theoretical on my part. I'm repeating what I learned from other people, who knew from first-hand experience. I couldn't write a song myself if my life depended on it. 
#6
When ur playing and trying to come up with lyrics it is difficult to come up with vocals that don't just follow the melody line.. I think it would help to just record and listen while writing lyrics. In my opinion Axl Rose is one of the best at doing that..