Have I been arrogant or caused something?

[Nitro Zeus]

I ask this question because today I went to my Christian mother's wallet and I took only my bank card with intention of going to net and see a doctor because I have huge nasal problems, and my Christian grandma saw me and she exposed me for no good reason.

My mother told me that I need to see face to face with a real life Doctor, not from Internet. Then I got mad and I said, "you know what? I already know a Doctor, and that Doctor is God" and my mom told me, "God does not do like, 'ok, let's heal that one', God heals people through doctors He left on Earth, not by His Hands". Then again this made me angry that I eventually said: "I hate my life".

So, have I committed arrogance? Have I caused my mom to commit a disbelief? Please tell me, I'm really afraid that I might have done something very bad. I hope it is not disbelief, because I don't want to be held responsible for it.