You have some misunderstandings about the expansion of the universe. I would recommend reading http://www.preposterousuniverse.com/blog/2015/10/13/the-univ...
The size of the observable universe: ~93 billion light-years
Time since the big bang: ~13.7 billion years.
http://curious.astro.cornell.edu/about-us/104-the-universe/c...
That doesn't mean he must be right, but I feel pretty comfortable citing him.