I have written an arpeggiated guitar which repeats over two chords, played finger style. When singing a melody on top, would this be counterpoint or harmony?
In the scenario described, it would be harmony. In essence, it's just two chords that happen to be broken up rather than played as a single block.
However, the broader question depends on context. Often arpeggios are used as a decorative form of harmony, but they can serve as counterpoint, which is a technique Bach uses quite frequently. That is, the arpeggio isn't counterpoint in and of itself, but the movement from one arpeggio to the next contains counterpoint.
One example of this is his Prelude in C Major from The Well-Tempered Clavier Book 1. Nearly the entire piece is a series of arpeggios, but each "voice" within an arpeggio corresponds to a "voice" within the next, creating a sense of counterpoint.
Listen here: YouTube
This can also happen within a single instrument. Bach again does this in his solo violin and cello suites. In the Prelude of his first Cello Suite, Bach creates the impression of counterpoint even though the instrument is only producing single pitches.
Listen here: YouTube
This type of musical texture with a single melodic line over a chordal accompaniment is called homophony.
Counterpoint, on the other hand, is known as polyphony, which involves two (or more) independent melodic lines.
Both homophony and polyphony contain harmony. In a polyphonic texture, the harmony is created by the interplay of the two (or more) voices, while, in a homophonic texture, the chordal accompaniment provides the harmony.
These terms are loaded. When the word counterpoint is used it connotes polyphony, multiple, independent, equally important lines, like a fugue. I suppose for some harmony connotes chords which some think means not melody, or something like that.
But, the simple fact is if you have more than one pitch simultaneously, you have multiple lines. The only question is about how much independence and melodic importance is in each line. The technical word for this aspect of music is texture. Usually four types are described: monophonic, polyphonic, homophonic, and heterophonic.
What you describe - a melody with chord accompaniment - is homophonic texture. In terms of multiple lines homophony usually has a melody, a bass, and chords. Obviously "the melody" is the most important line. The bass would come next, a good bass part usually has important linear characteristics (think walking bass,) the "chords" have the least linear importance, but they have linear elements too. For example, on guitar, an open
D to an open
A exhibits linear voice leading elements. The upper parts descend by step while the bass descends by a fourth.
You may notice I'm using the words line and linear. I'm deliberately trying to avoid the word melody, because that too is a loaded term. Some think of melody only as song-like lines. But melody is just a series of pitches with rhythm.
The question isn't whether your music is counterpoint or harmony. The music has both elements simply because you have simultaneous pitches. The texture is homophonic and the question is how much linear importance is given to each part.
When you play the chords in your song as arpeggios you raise the melodic importance of the part. Arpeggiating provides additional linear elements, the broken chord part gains direction and rhythm. Depending on the particular arpeggio treatment the guitar part could have as much importance as the melody part.