I'm not sure if you've done any chorus, and I'm not sure if you know your notes.
At the risk of making a fool of myself:
Do Re Mi Fa So La Ti Do, wasn't constructed to name the notes on the piano, we've got the alphabet for that. The syllables were constructed by monks in order to teach sight singing(seeing music on paper and singing the right melody).
Do was the starting tone, the Tonic. or the 1st, as Lisa put it. So, in Jingle bells, you stated the first note as Mi, which would be right if it started on a C. C(Do) D(Re) E(Mi). So, I guess I'm trying to say that the syllables are relative, move 'em wherever.
Now... in a song where you have a note, and you want to figure out a guitar rhythm to play over it. One thing that helps is to find the key. You've played piano, so I'm hoping you know your Key Signatures(The sharps and flats to the left of the treble clef). So, whatever the key is, say, E, like in your arrangement of jingle bells, that means that most of your notes will be inside that scale. E-F#-G#-A-B-C#-D#-E
That's the E major scale. So, if the melody is playing an E notes, (E E E, Jingle Bells) You can play an E Major chord over it. A major chord is constructed by the 1st note in the scale, the 3rd, and the 5th. In this case, E, G#, B. But unlike piano, on a guitar you usually hit octaves of your notes to get a fuller sound. An E major chord on the guitar is E(6th string 0 fret) B(5th string 2nd)
E(4th string 2nd) G#(3rd string 1st) B(Open 2nd string) E(Open 1st string.) So you're playing E B E G# B E. Or 1 5 1 3 5 1. They're just octaves of those notes. It's a triad, only fuller.
If I completely misunderstood your post, whoops.
If not, I hope this helps.