My mom and dad died 3 weeks from each other - everybody was saying I have to go and talk to somebody. Why? Would that bring my parents back and to be honest the more you try and encourage and preach for me, the less I listen. Some people benefit from it and some like me just don't. I am a very private person and will deal with my shit in my own way - maybe not the best way according to the books, but the best way for me.
There is no right or wrong way, I just know it was the darkest time I went through but I got through it and even though I will always miss them I can cope with it.
Only you can decide how you want to deal with it - there is no time limit and no right or wrong.
I am so sorry for your loss in such a short time. Good luck with the healing period. And do whatever makes your boat float.... for as long as you want. (just do not push your family away, but they also need to understand that you need some time by yourself and will handle it your way)
OK enough preaching - so you go and get yourself a beer or ten or scream or shout or hit something to make you feel better
Good luck - this feeling of despair too will pass , it just sucks big time.