I have been on TriNessa (norgestimate and ethinyl estradiol) Birth Control Pill for a month now. I noticed my face started to break out. Is this normal? Will it help my skin soon?

Common. Be reassured its actually fairly common for acne to "flare" when oral birth control is initiated. Give it some time to see how your skin will respond in the long run - this can be commonly on the order of 3 months. But as always, you should feel comfortable addressing this with your physician too!
Normal. Sometimes when you begin a hormonal treatment like birth control pills you may notice a worsening of acne. If it is not better in 3 months, talk with your doctor.