When Shiki awoke in the Game she had the appearance of her best friend Eri. She freaked, but in a happy way that made her really excited. Finally Shiki was who she wanted to be. She began to act like her, being all bubbly and cute. However, there remained a nagging feeling in the back of her mind; why did she look like Eri? Afterall, she hated herself. All her fears were answered when her and Neku were confronted by Game Master Yodai Higashizawa on Day 5.
It is here that we get to see the kind of person Shiki really is. She admits to being neither pretty or smart; there was nothing special about her. She hated herself. To get away from that she wanted to change, to become someone else––to be like Eri. However, when she got what she wanted, it didn't work. While she looked like Eri on the outside she was still the same old Shiki on the inside. She then realized she would never be Eri, but also discovered she never wanted to be her, and that she was just jealous. She learned what she valued most WAS herself, and that being Eri actually hurt. Shiki admits to being terrified of getting a second chance. If she were to come back to life would she still be jealous of Eri all the time? She didn't want that.
When she confesses everything to Neku he says to her that she is not Eri and that she'll never be Eri; she will only ever be herself. Even when she tries to argue back that Eri is better than her Neku tells her to forget about her. She needs to live her own life, and that if Eri can do it so can she. All that matters is that she tries. However, I think when she encounters Eri while she's in the UG and hears what she thought about Shiki, that she admired her for all the things she herself couldn't do and still considered Shiki her best friend after her death, that steels her resolve to change. Sure enough, when Shiki and Neku encounter the Game Master again on Day 7 all of her jealousy is gone and the two of them are able to defeat him and win the Game.
In the end I think Shiki became the kind of person she wanted to be. While she did not become like Eri like she originally wanted she instead became a better version of herself. She became someone who could love herself for who she is and make some pretty amazing friends along the way. Shiki doesn't need to be pretty or popular to have friends. As long she she's true to herself that's all that matters. It's not an easy thing to do so I think she's pretty incredible to do it.