Your parent keep bringing it up because your smell is offensive. They're trying to help you learn the things that will help you get a job, or have friends, or go on dates. In short, they're being a parent. Help them help you.
Yes. It is very important otherwise people might get very uncomfortable being around you. That creates barriers when making friends, getting jobs, etc. One other thing - deoderant is not the same as antiperspirant and vice versa. Use both.
I have sensitive skin and can't stand artificial scents, they give me a brutal headache.
When I get funky I dust my pits with baking soda. It erases smells instead of "putting lipstick on the pig". Wear a white shirt though, it'll turn your pits white.