my one of the sweet friends is a partitive construction. You wanted to mean one friend from your many sweet friends. But you have constructed the phrase incorrectly.
one of themy sweet friends is correct. Here one is a determinative and it's a Fused Determinative Phrase in that construction.
A genitive case of a pronoun (i.e my) can't be used before a Fused Determinative Phrase.
Therefore my one of the sweet friends is incorrect grammatically.