If you've been trained properly you should not have to look. You should be able to play by feel. All my music teachers, guitar, violin, upright bass, "encouraged" me not to look and that's putting it mildly. However, it does take years of practice to be able to play new pieces without looking at least once, especially if there are some novel fingerings or position shifts.
If you don't like looking at the wall close your eyes.
What part are you allegedly bragging about? Looking, not looking, sight reading, or playing something difficult? That comment confused me.
During performances one may have to look on occasion, especially of you are playing an instrument that allows you to move around on stage (like guitar). For me, looking at my hands for a "difficult part" is suicide. The second I look back I'm lost. In my experience training yourself to not look is the best thing you can do for yourself. So you say that you slow down the metronome and make a lot of mistakes. If you cannot play the passage or exercise at any steady tempo without mistakes then it sounds like you are without any muscle memory or physical beacon to guide you on arpeggios. In that case I'd say work it out without the metronome first, either by touch or looking, then when you feel you've got it start working with the m-nome.
My standard approach on something so new I can't even feel it is to work it out note by note, by feel, no m-none. Only when I can play it smooth and comfortably w/o a mistake do I start woodshedding it. For the most part I always play with my eyes closed or looking at sheet music. I am very grateful for the training my music teachers gave me.