Well, I'm mainly writing to say I'm currently experiencing the same kind of pain, and came to this page on the site try and find helpful information. So I don't come with any answers, sorry. I just picked up this new issue on my left hip about 1 week ago, and ran with it all last week. Occurrence of symptoms sounds the same as you...I'm OK during my runs, although i need a slow warm up, something like walking .5 mile and stretching. I ran hill repeats today and felt 100% OK. But after the run, as i cool down, the pain comes back, hurts when i'm sitting, and the next morning. I took a rest day yesterday but today was pretty much the same. I have a history of ITB tightness and pain, but lately it has been better as i've been using a self-massage technique to loosen it up. I also seem to have some tightness and minor related pain in my lower back on the same side, but it's very minor
What i think caused it was skipping stretching after a 5-mile run, which came 2 days after my long run of 10 miles. Instead of stretching, i went right into my garden and pulled weeds for 45 minutes, bent over at the hip...stupid, i know! After a few other injuries since late last year, I think i've learned to take time off to heal (2 months for achilles tendonitis), but in those cases, the injuries all hurt during my runs, and running made them worse. In this case, the runs don't make it worse, and I feel fine during...so i've continued. I'm concerned though that it will catch up to me. I have a 24-hour relay in September, and my first half-marathon in October, and want to build to those. If the pain was such that i couldn't run, i'd take time off immediately...
Anyway, i'm going to keep looking for answers, and might try to see my doc and some PT. I look forward to seeing any helpful responses to your post.
Tom