Another reply, for the sake of those perhaps finding this thread when looking for info on similar injuries in the future:
The regime of stretching and maximum dose anti-inflammatories seems to have worked. I decreased the dose after four days, and stopped taking them after a week. Though I can still feel the tendon in certain movements, and the hip still pops (like when you crack your knuckles) when I start up the stairs, it's not hurting any more. I'm still taking a herb in capsule form called Comfrey, which people in South Africa might be familiar with, and also rubbing Comfrey ointment directly onto the area where I had pain twice a day. In addition to this, I take cod liver oil (in capsule form) with my daily multivitamin. This alone can't fix things, but I believe every little helps.
I started cycling again this week, but only 6km on Monday, 8km on Tuesday, and 10km today. I'll probably stick to 10km tomorrow and Friday as well. Next week, I'm going to start running, but will be sticking carefully to a walk/run routine, then gradually eliminate the walking parts. I will cut back immediately if there's any pain. Stretching is now part of my daily routine, and I'm convinced it helped a lot with recovery.