So many of the things you are talking about resonate with how I felt after my Dad passed in 1998. He did not die of Alzheimers but a combination of physical problems that sapped his strength over a period of years. His passing though was still a surprise and I miss him terribly to this day. I am now full time carer for my Mum who was diagnosed 2010 with vascular dementia/Alzeimers.
Thoughts of 'why him?', 'what do I do now?', 'why bother?' all surfaced in the weeks/months following Dad's death. I could find no joy in anything not even my lovely daughter, my Mum, hobbies all were just endless chores that had to be endured. However going through the motions was precisely what I had to do until with time hints of meaning started to show through. Laughter, real hearty belly ache laughter, was a long time coming but it came. Waking up in the morning & not having my first emotion as dull sadness took time. I had many things to fill the void, my family needed me to function, my job, my animals. I understand you have no immediate family depending on you but would suggest perhaps you could consider some volunteer work. Just a few hours a week to start off with, you will have many skills that could help in many scenario's & give you the chance to meet new people. These folk may well be new to you and will want to know about you the marvellous wonderful individual that your parents made, and who they would be proud to see living a full life even while missing them both terribly. I still miss Dad and have little inner chats with him especially when Mum's having a bad day, but also when something good happens like just finding out I will be a Grandma. But I am so glad I knew him and all he has taught me about life and living goes into my putting one foot in front of the other every day! Reach out where you can, you will still have room to grieve, but this next chapter is about you, walk forward into your future taking all your lovely memories with you. Good luck! Mx