Hi yjackson, welcome to our community! You've asked a common question about how to grow your business. As you know, as our population ages, the need for home health care increases. You've already found out that it's hard to crack the obvious lead (hospitals) so you are finding you need to think "outside the box".
Have you reached out to individual doctors, retirement communities, and low income health care clinics? These would be excellent possibilities to start and may not already have affiliations. There are also many individual charities or churches that you may find would be open to the idea of providing lower cost alternatives to their clients or members. Some towns also have an advertising circulars or coupon mailers, that local businesses can use to provide a mixture of promotional pages and coupons. .
Since you're already active using social media, make sure you're making the most of it. We've got a couple of expert articles that I think you would find helpful 7 Ways to Boost Engagement from Your Social Media Posts and How to Optimize Your Small Business’ Facebook Page
Please let us know if you find these helpful, or have any additional questions. We have a great community here that hopefully will add their own experiences and offer some great advice. We look forward to hearing back from you soon, and getting to know more about you and your business!