Is it normal to feel sad and melancholic most of your days, without change?

No. Feeling sad most days is a sign of a mood disorder. Get a psychiatric evaluation!
No. Certainly, everyone has "bad days." but, if you are feeling melancholic most days, then it's time to seek out someone to figure out why and help you feel better. No one needs to tolerate being sad all the time: there is help out there.