I think you internalize your feelings, it's not that you feel nothing, it's that you've spent your life trying not to show how you feel to other people, even self-hatred is an emotion, but I think you struggle to express it to those around you when you aren't using a secure, anonymous outlet like this board.
I'm sorry to hear about your mother, and I hope all will be well, but try not to over-analyse yourself, that can be dangerous, if you are worried for and about your mother, then you are perfectly normal, sadness is a difficult thing to define, and the mind has strange ways of dealing with stressful situations, but beating yourself up over not feeling everything you expected to feel will only make matters worse. When my Dad had a heart attack, I was scared and worried, but I couldn't, in all honesty, define my feelings as 'sad' in any way, maybe because you can only fit so many emotions into a situation that looms that large in your life.
I can't tell you why you have problems expressing how you feel to those around you, that is for you to discover, but don't confuse that for 'not feeling', and don't think that admitting that you are struggling to come to terms with something is somehow a fault.
My partner was 27 when she met me, and I was her first companion, so you are a long way from alone in that respect, it's not a race, it's not a target, it's something that comes to you when it, and you, are ready, and never before, but not being ready isn't a failing, it's simply a sign that you still have things to learn and accept about yourself, sometimes it's better to stop trying to be who you think you should be, and start being who you are.
There's nothing outside of your own mind that can confirm to you that you are happy, there's no magic 'thing' to find that creates happiness, it's all inside you, and if you give up on yourself, then you are giving up on your only chance to find it.
I'm not a psychologist, but I do think you could benefit from telling someone who is qualified how you feel, if you can't talk to those around you, then maybe someone qualified, and totally removed from the situation could help, it doesn't mean there's anything 'wrong' with you, it just means that some people communicate their feelings better to complete strangers than those who they have to see every day.