I believe the core CPI figures leave out food and energy, since their prices are sometimes more volatile. So, the CPI does include healthcare and education, but I suppose those price increases must be outweighed by price decreases in other sectors.
[edit] In addition, there are "weights" for goods in different categories. Ex. in the document I found from 2013[1], the weights add up to 100, with housing-related items having a total weight of ~41.4. Healthcare is 7.5 and education 7.0.
So, the actual CPI numbers are somewhat manufactured. The weights correspond to what the BLS predicts the average family spends, proportionally, on those different goods. If your expenditures don't match those proportions, you will "feel" inflation at a different level in your own purchasing.