Songwriting has a weird place in the music world.  You don't have to play any musical instruments to write a song, it helps but not absolutely necessary.  You don't need to know how to read sheet music, again it helps, or even have great grammatical skills,once again ...  All you really need is an idea, a thought, a feeling or just an abstract concept.  If you are lucky enough to have an original idea, a rarity now-a-days, and you can hum a tune, you can write a song.  I am not saying it will be any good but it will be yours and there is something to be said for that.  Art for art's sake. 
        If you are looking to do a little more with your songwriting you should explore as many different genres of music as you can stand.  Surprisingly, gems appear in all locations and turning up something in an unexpected place is always exhilarating.  The more you are exposed to the different genres the more you will learn and the better your ear will become at distinguishing chord changes.  You will also get ideas for your tunes.  Don't rip off other artists, but one thought can lead to another, new, different thought.  You can expand on ideas, present the opposite or use an idea as a springboard for a whole new song.  Don't stick with Western music, meaning euro-centric stuff, try listening to the Middle-Eastern, Asian and Indian music.  It will be enlightening.
        Basically, a song is words put to music.  Everyone knows that.  But how come we still sing or at least know Stephen Foster songs (Oh Suzanna, She'll Be Coming Round the Mountain) and there are millions of other tunes we never hear,sing or care about?  I have always felt it was just the right combination of lyrics, tempo, melody and simplicity that make great songs.  Finding that combination is the trick.  It is the elusive Holy Grail of every songwriter.  Sometimes you are lucky enough to hit upon something good and that is great, but many times you end up with a mediocre or just plain boring tune.  That is ok, too, not what you always want but ok.  Put it away and start again.  The main point here is to explore and try different techniques, take chances.  You may hit something that sounds really good, a keeper.  If you like it, it can't be all bad.  I think it was Duke Ellington that said, "If it sounds good, it is good."  Amen to that.