Quality Cucumber

That's the question, huh? Composition is not an easy thing to do, nor is there one single way to approach it. Some people do melody first and then write the harmony, some people write the harmony and then the melody, others start with a rhythm, some do the lyrics first, some do the music first. You really can start anywhere yet end up with the same (or similar) result. In any case, there is usually some tweaking involved to get all of the disparate elements to line up.

I strongly suggest building a rudimentary knowledge of music theory and music notation. While this will not help you to compose in a direct manner, it will make it easier for you to hear the structures in your music and the music of others. This in turn makes it easier to diagnose compositional problems and work out a solution. (For instance, trying to figure out whether it's the melody note that needs fixing or the chord underneath it.) Here are some resources that bear my recommendation:

• musictheory.net - This website contains good lessons and exercises presented in a concise and orderly manner. If you can learn everything on the lessons page (and it isn't a whole lot), you will have built a solid foundation that will place you above most amateur musicians in terms of harmonic understanding. That is not enough to make you a great musician, or even a good one for that matter, but it makes you more critical and gives you enough vocabulary and understanding to articulate yourself verbally and musically.
  
  
• http://academic.udayton.edu/tobyrush...f/complete.pdf - This is a free PDF book that covers a lot of Western Common Practice harmony in a surprisingly small number of pages. The tone is informal, which is a nice change of pace compared to every other music theory text written ever, but the author also spends a lot of time shooting himself (and his students) in the foot. As an example, here's a garbage quote from page 2: "Music notation is the art of recording music in written form. Modern music notation is a product of centuries of transformation... and it is neither efficient nor intuitive!"
  
  I could write an essay about why statements like this are not only harmful to the student but also complete BS (If Mr. Rush thinks Western music notation is so inefficient and non-intuitive, why does it permeate his entire book?), but I'll spare you for now. Just be careful. It's difficult to sort the wheat from the chaff, and music is a subject where educators are not very fastidious to begin with. Not me, though. I'm hella fastidious.
  
  
• Hal Leonard's Pocket Music Theory - If you're willing to shell out a tiny bit of cash, this is an excellent little book. It's concise and provides [mostly] good information.
  
  
• If you get serious about this stuff, I highly suggst grabing a book that details "voice leading," which is the art of building smooth melodies that go from chord to chord. If you can grasp the principles of voice leading, composing becomes about 1000x easier. My favorites are Walter Piston's Harmony (4th edition or earlier), Stephen Kostka & Dorothy Payne's Tonal Harmony (5th edition or later), and Miguel Roig-Francoli's Harmony In Context.

Is this a technical issue (meaning you have difficulty singing while playing), or a musical issue (meaning that the notes don't sound right together)?

I'd need to hear you in order to make any sort of determination. Remember, as a composer, you have the unique perspective of witnessing music arise from literally nothing. Non-composers (AKA everybody else, including you before you were a composer) are accustomed to hearing music in its finished form. In its early stages, music is not at all impressive. It will be a while before it sounds like a finished product, and that's just how it is. Also keep in mind that you will have heard your sketches and noodlings countless times before the song is complete; it will sound redundant to you no matter what. Actual redundancy in the finished product can be an issue. Gaining a greater technical understanding can help you to recognize where the problems are and how to correct them.

The chord progression is king. If there is discord between your chord and your melody, then it is not going to be good. As a general rule, the main notes in the melody are also in the chord. For example, a Gm ("G minor") chord contains the notes G B♭ D. That means that the corresponding melody note should be either G, B♭, or D. There are certain exceptions which we call "nonharmonic tones," but even these facilitate movement to, from, and between chord tones. Here's an example, over the same Gm chord: G A B♭. A is not in the chord. It is functioning as a passing tone between G and B♭. Melodically, G and B♭ are the main notes of the melody and would thus be given more rhythmic priority (longer note duration, prominent placement in the measure, etc.).

You can also reverse engineer this process. If the main note of your melody is B♭, you can infer that the corresponding chord should contain a B♭. This could mean a great number of chords:

B♭ ("B flat major," B♭ D F)
B♭m (B♭ D♭ F)
B♭° ("B flat diminished," B♭ D♭ F♭)
G♭ (G♭ B♭ D♭)
Gm (G B♭ D)
G° (G B♭ D♭)
E♭ (E♭ G B♭)
E♭m (E♭ G♭ B♭)
E° (E G B♭)
C7 (C E G B♭)
Cm7 (C E♭ G B♭)
Cø7 ("C half-diminished seventh," C E♭ G♭ B♭)
C#°7 ("C sharp diminished seventh," C# E G B♭)
A7(♭9) ("A seven flat nine," A C# E G B♭)

And there are many many more. This means you have a lot of options in terms of harmonization. It is a lot of stuff to worry about, but this ultimately gives you more creative flexibility. Luckily, you can eliminate a lot of the candidates by considering which chords are in the key. That is a technical discussion which I will leave until later. I'm sure that this stuff is dense enough already.

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