E. E. Cummings wrote a poem called 'Puella Mea'. A quick skim of the omniscient google suggests that 'Mea Puella' might be more accurate. Which would be more accurate, in isolation, when used as a pet name for someone?
Both word orders are possible. Word order is flexible in Latin. It would be wrong to say that the Latin word order is completely free, but it is far more flexible than that of English.
In isolation, without further context, puella mea is the more typical choice. Latin typically puts adjectives (you could in see mea as an adjective) after the nouns, unlike English.
Furthermore, if the phrase appears in a poem, then metric constraints have their effect. I don't know the poem in question or even whether it was composed in an ancient poetic meter, but I remark that one can use puella mea in hexameter, but mea puella is impossible unless you insert other words in between.
Google might answer all your questions, but there's no guarantee that the answers are right.
Word order in Latin is fairly free, so neither of those is incorrect.
However, adjectives in Latin tend to follow their nouns. And skimming the L&S entry for meus, most of the attestations have it following the noun. The first word in a Latin phrase also tends to be more emphatic.
So puella mea is more neutral, while mea puella is closer to "my girl". But neither is incorrect, and especially in poetry (where the meter tends to constrain the word order) neither would be considered strange.