Is it normal to not feel empathy, sympathy or love?

even when i was a kid my teachers noticed that my empathy was lacking....whenever a friend fell or something bad happened to them, my mind was blank.....completely and utterly blank from any emotion. it continued like that for years......me being blind to this lacking empathy until one day....my Nana died. i was so close to her, she was like a second mum to me and when i found her body my mind was blank. i just didn't feel anything. when the ambulance came, the man asked if i was ok. he was surprised that i wasn't sad at all when i replied with "im fine". he said i must have been in shock but after three weeks passed i STILL didn't feel anything for her passing. now for sympathy. in my teenage years friends would come to me with there problems and i would just get awkward and say something cold or impersonal. once my friend came to me for comfort because her aunt died from cancer. i replied with "well it was for the best" and she flipped, saying i was a monster.....a heartless monster.......and that is when i started to question if there was something wrong with me. during that time i had a couple of /lovers/ so to speak and no matter how much they loved me, i simply felt nothing toward them. even if i tried to love them i still felt nothing. every kiss, blank, every time we met up, BLANK AND EVERY TIME WE WOULD HOLD HANDS STILL NOTHING........as you can see this is getting to me.......im starting to believe i am a heartless monster. so the question is.......is it i normal to not feel these emotions?