It's pretty good. "Arms of her" is wrong, it should be "her arms." As written, it is in the present tense--you do it now. If you mean to put in the past tense--you did it when you were a child--it would be
"I often nestleD in HER ARMS listening to her nursery rhymes quietly."
That's correct and natural, but as a matter of style--other native speakers might NOT agree--I'd put in a comma and change the word order slightly:"
"I often nestled in her arms, listening quietly to her nursery rhymes."