According to this paper http://www.ncbi.nlm.nih.gov/pubmed/23829164 there are approx. 3.72×10^13 human cells in our body. Thats around 100000-times more cells than you estimated 🙂
Accordingto this source (http://sciencenetlinks.com/student-teac … your-body/) there are approx. 200 different types of cells, each containing 20 different types of structures or organelles.
Interestingly, we carry about 10-times more bacterial cells than human cells in our body at any time! Our intestine alone harbours around 500 different species of microorganisms.