My mom doesn't care but it's really fudging annoying me

What do I do? Everything I say to my mom, she thinks it's nothing and I'm overreacting, but it's usually red and splotchy in those areas and it makes me self cautious. They won't listen to me. How do I get rid of them? I would try and get to a dermatologist or something like that, a skin person, but I can't because I'm too young to go anywhere but target and my grandmas house by myself. I also have tiny white dots (not acne, tiny dots, too small to get a clear pic of) all across my nose, which makeup lookes horrible on and it's really rough skin. I already use coconut oil when I need a pick-me-up on my skin, but it doesn't help. I have an extremely oily T-Zone. I currently use target brand cleanser, I tried the clean and clear cream one but it made my face burn way too much and it worsened my acne. I'm getting paid for good grades, so I can buy any certain thing myself, but I just need to know what to do first. Thank you!