Qualia the Purple (warning, TV Tropes) written by Ueo Hisamitsu. Both the original novel and the manga adaptation have an English adaptation by Seven Seas Entertainment.
Hatou Manabu (nicknamed Gaku) has a very odd friend at school named Marii Yukari. Yukari has purple eyes and a bizarre way of looking at the world: she sees all other living things as robots. This has not always worked out well for Yukari, even costing her a best friend when she was younger. However, Yukari insists that the things she says she sees is true, and her vision seems to give her insight into the abilities of others.
Gaku thinks she's just weird, but she soon realizes that Yukari has unexpected talents. It seems she can fix anything, and even the police come to hear her insights. It turns out that Yukari's purple eyes are not unique in the world! However, there is one important distinction among those who see humans as other objects. Do humans appear as unimportant as objects, or do those objects appear as important as human beings?
Starting as a seemingly lighthearted series with a sci-fi premise, it quickly makes good use of said premise, turning much darker soon enough. The fast genre shifts and the surprisingly detailed use of physics concepts are some of the most prominent characteristics of this work.
The Cell Phone arm is mentioned a few times, such as:
Cursed with Awesome: Gaku's cellular phone arm. She can use it to talk to parallel versions of herself. And it functions as a normal phone, too. But she is its battery, and overuse leaves her physically drained. She keeps sugary snacks on hand after she loses two pounds in one day from making too many calls.
Mention of her becoming a god-like entity:
Earn Your Happy Ending: Gaku's plan on doing whatever she can to finally obtain a world where Yukari doesn't die. It's just that multiple attempts of it have failed repeatedly. One of the universes has an earned happy ending to it. Hatou has practically become a non-existent-existing god-like entity that is watching over evolution and life on earth. Finally, Yukari is saved from JAUNT and does not painfully die. And she's the only one who can talk with Hatou. Yukari is horrified that her friend has opted for this type of existence just to save her and wants Hatou to return to her. Hatou, remembering her life as the regular Hatou Manabu, manages to break free from her strange existence and regain a body, kissing Yukari and the two are finally together.
Your description reminded me that I'd read this on TV Tropes, so I searched for
phone arm, and found Qualia on the first page of entries.