Is concealing a mobile phone from one's mother while playing with it considered showing off, and does it fall under major shirk?

What you mentioned is neither showing off (riya') nor polytheism (shirk). For a Muslim to conceal his mistake out of shyness before Allah or people is Islamically مطلوب (required/desirable), and the Prophet, peace and blessings be upon him, encouraged it by saying: "All of my Ummah are pardoned except for those who publicize (their sins)." However, you should have been truthful with your mother and not deceived her. You have done well by repenting and striving in your studies.