I am a doormat to other people
A door mat? What do you mean?
I don't know how to say no, I'm a nice guy and it makes me feel bad when I have to say no
It's great that you're such a nice person and it's a rare thing nowadays so you should be proud. That being said, stand up for yourself more. There's nothing wrong with saying no to requests you don't want to do.
I should be saying no and I'm a bad person for not doing that.
No, you're not a bad person at all, you are extremely kind! Don't let people get you thinking otherwise. I believe though you need to think for yourself and your happiness instead of other's sometimes since you deserve a break.