It depends on the program.
For example, some programs like Hopkins and Harvard usually accept only people with a doctoral-level degree or full-time work experience into their MPH programs; these same schools will frequently accept people with less work experience into 2-year master's degree programs (e.g. MSc, MHS). Most other programs aren't quite as picky, and will accept people with varying degrees of work experience.
In your case, most schools will appreciate the work that you've done at the hospital and as a pharmacy tech, and will count this in favor of your application. It probably won't be viewed as full-time work experience, but don't sweat it. Except (perhaps) for the two MPH programs I mentioned above, don't let this deter you from applying. Many people apply to public health programs shortly after undergrad, and many have had only short-term internship-type work experiences. Link your experience to your interest in public health and your career goals in your personal statement (if they relate), and/or focus on your future plans. Assuming all the other aspects of your application are in order, your relative lack of work experience shouldn't be a problem.
Best of luck!
