Sorry I didn't notice this earlier. My hips were bothering me something fierce around August, and like you said, you really can't do much of anything when it's the hips, for me just trying to stand up was tear worthy. But I found that a heating pad worked better than ice. While the general rule of thumb is ice the swollen and heat the sore. With bursitis ice can actually make things worse, or at the very least inhibit healing.

You were probably right to get a wheelchair for getting around inside the house, but laying down is the best, and since its just one hip, the best thing to do if you can is laying on the opposite side with a pillow or rolled up towel between your knees, whatever works to place your thigh and by so your hip in a neutral parallel position. Place a heating pad (the microwaveable rice/buckwheat bags are best for the little bit of weighted pressure they apply) over the affected area, which likely not only includes the hip but the lower back muscles as well.

Rest for a good 15-30 minutes like that to relax the muscles, if it swells a bit from the application of heat, ice the area for no more than 10 minutes (avoiding the lower back) allow the skin to warm back to about normal temperature and apply the heat again. When the muscles seem to have relaxed some and the pain has diminished some gently massage the area if you can, if it's still to painful, continue applying heat/ice until it can be touched without discomfort.

After gently massaging the area, roll to your back and use a rolled towel, holding the ends of it, wrapped around your thigh and gently pulled your leg up and towards your chest (don't pull it into your chest, a few inches to a foot off the bed is fine, your just trying to get circulation back to the joint and stretch out the muscles a bit.) try your best not to use your leg when you lift it, but use your arms to do the lifting, you want to move the area but not tax it.

Roll to your side and relax, repeating the above steps as needed throughout the day and avoiding sitting or standing for long periods especially since it's a side you already use as your main support. And once you're feeling up to it, I would definitely ask your doctor about some pt, even if they can't do much to help out the right leg, they should be able to help you strengthen the left and learn the warning signs that you're over-exerting it and setting yourself up for another attack like this.