Myofascial pain and dysfunction is a possible cause to what you describe.
Gluteus minimus muscle can radiate pain all the way to the calf and foot. The pain may effect the strength in the radiating area. Muscle pain in the morning is not common unless inflamed or sore. The pain reducing after a while might be due to a better circulation to the affected muscle.
Inactivity is a possible cause to myofascial pain dysfunction as well as running(long term stress).
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