Is it normal to not have empathy or sympathy for people?

No youre not a sociopath. Yes its normal.

i also feel the same as you. i was like that when my nana died. she was like a second mum to me and when she died i was blank of all emotion. every one around me was grieving and like you i was completely fine. so just know that your not the only one out there feeling this way.

This is called narcisism. All people have some level of it. its part of self preservation. But when its out of balance as in your case, it is a severe lack of empathy. You care about yourself more than those around you . Your reflection in the mirror is what is most inportant in your life.

I "often" don't feel guilty about things either.

That line showed you not to be a sociopath. They don't suddenly feel guilt, then rest of the time don't, and so on.

Somebody else asked this question and I just typed this answer to them. I'm considering pasting it onto a word document and saving it onto my laptop to paste on because this question is so common that I don't think I need to keep taking time out to type responses anymore because atop your lack of concern for others you also have trouble following directions. I added a little for kicks.

And this question has been asked before. At least four or five times a week. You honestly think that this is special in the world of humanity? People kill each other all of the time, steal from each other, discriminate against each other, CEOs make decisions that have put millions out of jobs and they still sleep soundly at night, teens brutally bully other children in school, often to the point of suicide while children allow their old lonely parents that sacrificed a huge hunk of their lives for them rot and die in nursing homes and you wonder if you're somehow special for not having feelings for others? If anything, you're part of the majority.