I'm so sorry you are going through this. I can't speak to the BP meds issue, but I have a few thoughts for reducing pain without medication. Two things have really helped me - restorative yoga and MBSR. Restorative yoga is NOT the typical yoga thay tends to pop in people's minds when they hear yoga. Instead, these poses are designed to help your body heal and relax. You lay in a pose for 20 minutes. I took a 2 hour restorative yoga workshop and it was the first thing to move the pain down for me besides meds. The other thing has been the Mindfulness Based Stress Reduction course I'm taking. There is an online version of the course and a workbook you can do by yourself if a class isn't an option. It's more than meditation, though that and gentle yoga are a big part of it. Meditation by itself may be an option and the creator of the course, Jon Kabat-Zin, also made a Meditation for Pain CD you could look into. I was super skeptical of meditation and resisted it (and didn't do much of the homework), but it has really opened up space to make the pain more tolerable.

To be clear, I do take pain meds. But between yoga, meditation, and acupuncture, I hope one day to cut back or eliminate medication. Hope this helps and you find a solution soon!