The back of her right hand, of which arm's elbow rested on the door panel, pressed against her lips.
The context is that she was weeping with stifled sobs, and smothered her sniffs.
My concern however regards the use of possessiveness, inasmuch as not to sound too vague, but also not to exaggerate with dropping a ton of them in a single sentence.
Surely there's no hand to have an elbow, an arm has such articulation, unless we rename wrists to elbows, which is not the case.
Does this sentence above look fine from a native speaker's point of view?