If your community has an AIDS resource organization, perhaps you could start there. The city I worked in had a center that solely cared for people with HIV, a food pantry, nursing clinic, pharmacy, counseling, social work services, legal aid help, needle exchange, etc. It was not a hospital. With the meds that are available for HIV folks now, hospitalization isn't as necessary as it once was.
I started working with HIV by anonymously testing at risk individuals in the community. The funding came from a CDC grant, which was allotted to our state. (I answered an ad that was in the paper, as odd as that may seem.) I worked at a small not-for-profit STD clinic.
Our community has a med school and they have a clinic especially for Infectious Diseases with HIV being a primary focus.
Many AIDS organizations do need volunteers but as far as paid positions, (in my area), are few and far between. Maybe volunteering would allow you to at least get your foot in the door.
It is a rewarding specialty and I do hope you find something. I feel like I was blessed to have the position and opportunity I did.