If you don't already know about it, you can check out
this page.
When you have a motif, there are three (and only three) options you then have: 1. repeat it, 2. vary it, 3. add something new.
That's it. That covers
all of your choices. But even though it may not sound like much, it actually encompasses a great deal of possibilities. You can imitate it, invert it, retrograde invert it, change the note values, change the notes but keep the rhythm, change the rhythm but keep the notes, etc. But trying to develop all of your ideas at once is a good way to drive yourself insane so I'd recommend picking just one, no matter if you think it's fantastic or dull as dirt, and trying to do everything you can with it. I think it would be better to begin as simply as possible. Find a motif that can fit in one or two measures and see what happens. The website I linked to can give some pointers here.
This is exactly the sort of thing the greats did. The beginning of Beethoven's 5th Symphony, for example, is just the same four-note motif used
over and over and over again. The thing is he stretches and transposes it so much that our interest doesn't waver.
In terms of apply this to entire songs, you can always practice with antecedents and consequences (aka
a phrase). Again, you can start out small: write a four bar phrase and "answer" it with another one, then repeat that first phrase and "answer" it again but this time with variation (often through a change in the chord progression).
You said you got those chords by flailing around on the keyboard. Suffice it to say this is not an ideal way to compose. I don't know how much theory training you have, but you really ought to have some fundamental stuff like the movement of diatonic chords (though it would be better if you knew many more chords than just diatonic ones) if you're going to continue writing music. If you want I can refer you to some more websites.
Do yourself the kindness of not worrying about completing full songs right now. Build up your strength (and confidence) one step at a time and your music will be all the better for it.