Good, I am happy you did not fall, and I hope I can help you here. Please understand that no one online can state anything with certainty, all I can do is offer my best educated guess based on what you wrote.
And from what you wrote it does sound like you pulled that muscle when you tripped. Heat is great for a spasming muscle, the heat will relax those taut muscle fibers. Some people find cold can help as well, but cold can tend to make it worse for some; cold is more for a physical trauma...if you had hit or banged the area. Rest is good as well; if it were a an ankle or a wrist I would suggest elevating the limb...but thats not possible with a hip.
As long as it is feeling better I am relieved. The fact you can walk well makes me feel better and more confident you did not do anything horrid to yourself. If the pain comes back though, or gets worse or agonizingly severe, or difficulty urination, I would suggest you get checked out just to make sure you did not do any more damage than just a muscle pull.
More information on muscle strains: http://www.webmd.com/fitness-exercise/guide/muscle-strain
I hope you continue to feel better,
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