Google has a new Dataset Search, where you can search for datasets on specific topics. Not everything this search will find is free to access, and it only finds a very small proportion of what exists(it won't find most of the datasets the library owns, for example). But it's one place to look for health data.
People often use these words interchangeably, but they refer to different kinds of information. Knowing which one you are looking for will help you figure out where to search.
Statistics can take the form of percentages or other quick facts presented in an article. They may also be presented in charts, tables, or graphs. Statistics are already analyzed--they are intended to tell you how much or how many of something there is. If you are looking for a quick number on something, you're looking for statistics. The graph below is a good example.
From: National Vital Statistics Reports, Vol. 65 No. 4, June 30, 2016
Data are the raw materials from which statistics are made. They can take the form of datasets or machine readable files for statistical or textual analysis programs. If you're looking to understand why or how something is happening (and you want to do this research yourself, not read what someone else has written), you're looking for data. The spreadsheet below shows one example of what data might look like.
Center for Disease Control and Prevention. Reported cases of Lyme disease by state or locality, 2005-2015.