I want to do more as a Muslim

Assalamualeikum!
My name is Nour Al-Rawaz and I am 19. I was born in a mixed family with a mother who was a Christian, but never really felt Christian or did anything her religion told her to. My dad is an arab Muslim. My siblings and I are also Muslim, but have never been practising Islam, because it's never been something we were taught. We always fast during Ramadan, we believe in Allah, we celebrate Eid and we know a couple of Surah's, and that's about it. Whenever someone asks me about my religion I always say I'm a muslim, because I feel like one. I believe in Allah and in the Quran. But recently I've been having this feeling that I am not a good Muslim. I mean... I don't do prayers, I don't go to the mosque, I don't wear a scarf (Hijab), I wear short sleeves and vests... and recently I've been feeling like I'm not what a real Muslim is. I am Muslim in my heart, but don't know if you understand what I mean. I feel that I don't do the duties a real Muslim should. My mum converted about 7 or 8 years ago in the central mosque of Aleppo, Syria. But still, she believes in the concept of God, but never really called God "Allah". She's never fasted, never prayed, wears bikini on the veach, rarely drinks and smokes. As you can tell she is still living the life she was before she converted, so nothing has really changed, My dad prays 5 times a day and goes to Mosque on Friday. He always fasts during Ramadan and does not drink. I would say to me he is a good Muslim. He doesn't really like the Idea of a Hijab though, since he does not believe it says it anywhere in the Quran that a woman should hide her hair. So as you can see things are strange with my family when It comes to religion. My mum is a bit against us fasting because she thinks it is unhealthy but I told her it is my decision and she respects that. I want to do more as a Muslim but I don't know how to start and what to do. It is extremely difficult for me, mainly because I feel like my mum and siblings would secretly judge me if I start praying.