I understand the struggles of finding your first entry level job. It seems that even entry level jobs want you to already have 2 years of working experience in the field, which makes you wonder how to even get started.
My best advice to you is to make a LinkedIn profile if you don't already have one, and then start building your network. Search for job positions in your area for the positions that you're interested in, and then send a request to the recruiters who are in charge of filling the positions. You can then also personally send them a message to introduce yourself. Even if you don't fit the particular position listed, they may have other positions available or may refer you to other recruiters. Also be open to contract positions, as that is a common way for a lot of companies to "test out" someone for a period of 6-12 months to see if they're a good fit before offering them a permanent position.
Remember that there is an option on linkedin to make your profile openly available to recruiters to let them know that you're seeking employment.
Another helpful advice is to join any public heath societies or groups in your area and start networking there. The career office at the university where you graduated from may be able to help you with that.
Once you start having more experiences on your resume, you will have an easier time getting responses to your applications, but for entry level positions, its really about who you know and who's willing to give you a chance. It's crucial to Network Network Network
Gary recommends the following next steps:
Sometime the things we search for are nowhere near us remember that. I would advise you to go on glassdoor.com, idealist.org and indeed.com to look for jobs related to public health. For example healthcare administrator, health and safety engineer and or research analyst. Every good thing requires patience infact there are people who have graduated college 5+ years ago and still have not been able to find work in their field of study. I believe in you and I know you will make it. I wish you the best on your journey.