My health anxiety is starting to get the better of me. recommendations for managing it without a prescription medication?

Find a life coach/therapist that will teach you the skillset needed to manage stress/anxiety. While you work on it you may discover an underlying subconscious issue (about something else entirely) that manifests as health phobia. It is easier for our conscious mind to accept a focus on health than it is on what others may not consider important.

Have found very beneficial outcomes secondary to therapists who are skilled in Cognitive-Behavioral therapy, and use of Biofeedback therapy has also been helpful. You might also find meditation to be useful, but it takes time and dedication to learn mindfulness.