Running injury / recovery

I'd like to start by saying that I will be discussing this with my doctor, too, but there is so much knowledge on these boards that I wanted to put this out here as well.

I've been running regularly for a few months. After experiencing several hamstring strains while doing C25k, I met with a running coach who suggested I start out even slower. He put me on a training plan of 15 seconds running / 90 seconds walking, up to 10 intervals per run, 3 - 4 times a week. Each week I could increase the running time by 15 seconds. Under this plan, I was able to get up to 1:45 running, 1:30 walking with no issues except some foot pain that was resolved by getting new shoes with a wider toe box.

Last weekend I was going to run / walk in my first 5k - I got less than 1/10th of a mile in and something in my hip popped (in my head, I "saw" a rubber band stretching, then popping back), and I could barely walk. I should mention I was running downhill, and stupidly leaning way backward to slow myself down, so my feet were landing way in front of me.

I went to the ER who confirmed nothing was broken, and I set a follow up appointment with my regular doctor for tomorrow, when I might get some more specific information about what happened. One week later, I'm at least able to walk with no pain. I'm fairly certain I'll be told not to run for at least six weeks, and am considering putting that moratorium on myself if my doctor doesn't, because I've never done any strength training and I think that really contributed to this injury... Which finally brings me to my question!

If I choose to focus the next six weeks on strengthening my hip and supporting muscles, does anyone have any suggestions for exercises that focus on running strength? I have access to a gym with some machines, but no free weights. I work full time, have kids, and go to school half time, but I can commit to about the same amount of time I was committing to running / walking (1 hour a night, 3-4 nights a week). Body weight exercises / stretching routines that I can do at home would be even better, and would allow me to work out 5-6 nights a week. All suggestions / links welcome. Thank you in advance!