New to music theory, am I right?

[Wurlitzer]

The question of whether D or G is the tonal centre is simply resolved by (a) what note the melody resolves onto and sounds finished on (and, usually, actually finishes on), and (b) the relationship of the chords to the phrasing. Your ear, sense of melodic impulse and awareness of where phrases are "arriving" tell you immediately whether a chord progression of D - G is I - IV in D or V - I in G.

The OP has said it's in D, so those factors are clearly adding up to that, for him, which is good enough for me. As he wrote the song and decided how and when each phrase resolves, I can't imagine why he would be wrong. In fact I can't see how he even theoretically could be wrong. If he's feeling it in D as he writes it, then it's in D. The only question is what exactly it's doing around D.

But sure, listening to it or seeing a score would resolve the question for those who believe theory is something to be externally imposed upon the compositional process, rather than something to illuminate it from within.

[GilesAnt]

Since the OP is uncertain about the key/modality of his music, we can't assume he is right about the tonal centre of D at the beginning - does he simply mean a chord of D or a whole passage containing other chords as well?. If he knew, he wouldn't be asking.

It's not particularly a question of deep theory, it's just that given what he has told us there are two leading possibilities.

Incidentally, the melody is not necessarily the best guide to establishing key, since a given note may be part of many chords. A melody may be harmonised in different ways after all. Many composers actually exploit this ambiguity of keys and tonal centres to challenge the ear. Hence there is not always a 'right' answer.