In Pygmalion, in what ways did nature cause Eliza to suffer?

It is hard to see Eliza's conflict as one in which nature rather than society or other people is most responsible. Other people's prejudices against lower-class individuals and society's rigid control over who can move up within it relegate Eliza to the lower rungs of British society. From there, she has little hope of moving beyond selling flowers on the street.
Nature might play a part in her breeding, as she inherits her status from her father, also among the lowest of classes, yet he is brought on stage specifically to demonstrate a delightful critique of "middle class morality," which keeps his sort in contempt and too impoverished to offer a moral perspective on what his grown daughter is doing in a professor's house.
Indeed, from her father (or nature) Eliza seems to have received physical beauty, which aids in her transformation. With a bath, some elocution lessons, and exposure to upper class manners, she is able to pass as one who belongs to the very highest of social tiers. Had she been an ugly flower seller, one wonders if she would have been able to do this, or whether Higgins would have wanted to bother with his experiment.