I think there's something wrong with me...?

I'm spelling things wrong that I know how to spell, I'm adding things up wrong that I know how to add up! I can't sleep when I need to, I'm lying there for what seems like hours trying to force myself to shut off. My eyes feel heavy a lot of the time but I'm guessing that is because of my irregular sleeping patterns. I have also had a cough for almost two months now, sometimes it's completely dry and sometimes it's very tickly. I know I should see a doctor but I'm only just 16 and my Mum thinks I'm being melodramatic. Thank you whoever can help, I'm so confused.