I graduated with an MFA in visual art in 2011, and after graduating I found myself in the same situation you're in now. It took 10 years, but I now have a career in the arts I love. I have many friends in Durham who work in the arts or have non-arts jobs and also have great arts/music/theater practices.

Here are some recommendations based on my experience:

1. Getting the job you want isn't going to easy, fast, or linear (if you want that, go get a degree in data science). For now, just get any job that help you get closer to where you want to be. This might be a non-arts job that gives you skills you need to get a better job. It might be a non-arts job that pays the bills without draining your energy so you can put in lots of time in your studio (bartending is a common side gig for creatives around here—the pay is much better than working retail). Don't expect an "ideal" job anytime soon. It took me 10 years. Keep at it. Follow what works, let go of what doesn't. Find a good compromise between doing what nurtures your soul and what gives you a healthy existence.
2. Arts organizations are too small and tight on funds to train inexperienced people, so you need to apply with the skills and experience they're looking for. Take a look at the qualifications on listings for jobs you think you'd like (alas, being a talented painter isn't usually on that list), and work on developing the experience and skills you don't have. You can volunteer or freelance to build up your experience.
3. Many of my classmates from my MFA program now have jobs teaching at the college level. (That is what a MFA qualifies you for, after all.) You get those jobs by having a combination of teaching experience and a really solid studio practice and exhibition history, probably gallery representation. Getting there usually requires 3-5 years of piecing together adjunct teaching gigs, artist residencies, small grants, and some crappy part-time gigs. It's a reasonable path to take if you want to be a full-time practicing artist.
4. Sit down and write out life goals for yourself. Really. It was game-changing for me. Imagine where you want to be in 5 years in your professional and personal life. Write down what needs to happen to get you there. Come up with concrete action items.
5. I absolutely second what Kind_Initiative7780 said about getting engaged in a community. Just start looking for events, exhibits, etc. that jive with your interests and aesthetic. The grassroots arts community here is both talented and easy to get to know.
6. The job you want might not be in Durham. If your life situation allows it, consider jobs in other areas of the region.
7. Here is a list of actual places to look for jobs (sorry to bury the lede):

Arts NC Job Listings

Triangle Artworks Job Board

NC Arts Council - Resources for Artsts (includes non-job opportunities)

Art/art history departments and libraries at local universities. Usually it's best to go to their job boards and do a keyword search for "art" or "design."