Great question! I cannot, obviously, write an essay for you, but I can provide you with some pointers.
The unifying element that I would identify that joins Juliet from Shakepeare's Romeo and Juliet, and Nora Helmer, from Henrik Ibsen's A Doll's House, is an epiphany of self-awareness.
For these two pieces of literature, that which seems to be the most impactful in comparing these two women is how they take command of their lives.
Juliet changes when the Nurse advises her to turn her back on Romeo—her husband—and marry Paris, even knowing Juliet has sought the blessing of the Church to sanctify her marriage to Romeo. She is chaste and a pious young woman. The Nurse suggests that she turn her back on her vows and her husband, vows made in her heart and in the eyes of the Church. From here on, Juliet does not include the Nurse in her plans with Friar Lawrence. The Nurse gives her advice at III.v.213. Juliet makes her decision at III.v.236.
At this point of the story, Juliet must learn to stand on her own two feet and depend on the life she can make for herself. In this scene, she has not only lost the support of the Nurse, but also her father. Only a day or two before he had told Paris he must wait for Juliet for two years to marry, and then only with her agreement (I.ii.1-34); he has now completely changed his mind, demands that she marry Paris, or he will kick her out into the street. Even her mother, who argues that the wedding seems too soon, and that her husband is unreasonable, changes her mind as well, telling Juliet she (Lady Capulet) is done with her (III.v.107-204). Juliet knows she is now a wife and grown woman, and must go on in the absence of Romeo.
On the other hand, Nora is older than Juliet, is married and a mother. Her maturity has been stunted by her husband who repeatedly treats her like a child: he chides her if she eats sweets, demands she tell him everything, and does not allow her to have an original thought. For example, when Dr. Rank appears after the dance to say his farewells, (which is only certain when they see his cards in the mailbox with an black "X" on them), Nora and Rank have a brief discussion about what kind of research he has done, which will give him the answer he needs to know as to how long he will live. Torvald Helmer, Rank's "best" friend, not only has no idea how serious his situation is, but belittles Nora's knowledge in Act Three. When she asks about Rank's scientific work, Torvald jeeringly says:
Just listen!—little Nora talking about scientific investigations!
Nora does not seem to notice. However, when Torvald discovers the things she did (to save his life), all he cares about is his reputation. He is furious with her. Her eyes are opened at last. Whereas she had feared that when he found out, his love for her would make him sacrifice himself for her, she finds now that he sees her as having ruined his life. He insults her ("a hypocrite, a liar...a criminal"), and he promises she will never be allowed near the children again. It is at this point that she realizes several things: how badly he has treated her all along, that she does not know herself, and that she is compelled to find a way to survive on her own.
Both women know they can only depend on themselves. The realization of being alone is wrenching, but rather that giving up, each has an epiphany of sorts: becoming self-aware and determined to move forward.