One of two likely problems come to mind regarding your responses. It definitely sounds like it is more extensor related than hip flexor. However the culprit is most likely the fact your hip flexors are dominating your back extensors which predisposed you to the strain.
It's hard to narrow it down too much without over-speculating, but it sounds like you strained either your multifidus or your quadratus lumborum. Both of these muscles are located near the side of your lower back.
Your QL is a MAJOR postural muscle for activities like walking and running because it actively keeps you upright during those movements. It also works as a back extensor and lateral flexor of your spinal column (both of which you have pain with).
The multifidus is similar but smaller and deeper to your QL. Even though it's smaller it's a very STRONG set of muscles. The reason I am suspicious is because of the amount of muscle guarding you have. It's main purpose is to protect and support the spine so weight is distributed evenly between the discs; this means that before you do movements like extension/lateral flexion/etc, it's ALREADY activating in anticipation of those movements. Say you were about to get up from bed and you contracted your abdominals to sit up -- boom, back pain. It's already bracing in order to initiate that movement.
I know this is annoying to hear but the best thing to do is avoid running or any other impact activity (esp with hip flexion). I had a very similar issue over winter break and it refused to go away until I eliminated certain stressors. If I did the wrong movement (usually side bending or extension) it would set off a lot of guarding.
1. Get rid of all muscle guarding. I ended up spending 2 weeks in PT only to get pissed at having to spend 20$ co-pays for no relief. I stopped going to PT and got a tens unit on Amazon (mine was 65$ for a really nice portable one) but you can get very similar ones that will do the trick for about 30$. I used it about 3-4 times a day and it REALLY helped calm down the guarding. The less guarding I had the quicker my back loosened up and also the more mobility I had.
2. Avoid stretching the muscle. My chiro and also a PT kept insisting on doing this and every time I did their stretches my back would flip sh*t. Instead, I eased my way into activities that had slight hip flexion (elliptical with low incline). Then a few days later I started jogging/running but at a slow pace with lower hip flexion.
3. Massage. Massage. Massage. SO much more effective than stretching for a back muscle. Plus who doesn't love it? It will help get blood flow to the area and also loosen up any further tension/guarding.
I do have some good rehab exercises for back extensors and core but it's important that you get rid of the muscle guarding first otherwise you'll stay in a vicious cycle. Back muscles are really a b*tch to get under control but if you consistently baby them for a good 7-10 days you'll get over that hump and be OK. Shoot me an e-mail and I'll forward you a document or two with exercises I have saved.