Ok, then concerning pencil and paper, I assume that you already understand that the melodic minor Key Signature is the Same as the relative major. So, the Db scale has 5 flats in the key signature. So does Bb melodic minor. Then when, when starting the Bb melodic minor scale, all you do is raise the 6th and 7th tone by a half-step, which means, in terms of writing the scale on paper, writing the 5 flats indicated for the key signature, and then writing in a natural sign on the G (the 6th tone of the scale) and another natural sign on the A (the 7th one). Surely, if you understand this, it shouldn't be difficult.
writing a melody that feels convincing can be a tricky thing. One shouldn't judge too harshly one's initial efforts. There are different ideas I could mention, but there are many ways into that world, and different ways work for different people. So you mention that about having powerful ears . That's a good thing as it relates to composing. You might think of a mood, sit with it, and see if you imagine a melodic line , or a fragment of a line. It might not come right away. You must sit with it. Lightly experimenting with your voice to mimic what your inner ear is telling you can get the ball rolling. This is just one approach to opening a door. There are many others. I could go on, but this can be involved, and you may need a teacher who really knows how to navigate this in a meaningful way - so that you become energized and wonderfully enmeshed in that exploration of composition.