Heel pain. Sounds like you may have bilateral heel spurs or plantar fasciitis. If the pain is more towards the heel it could be a spur. If it is more mid foot - the plantar faciitis is more likely. As we sleep the tissues that create the arch of our feet contract ever slightly - first thing in the morning when we get up - there is a "springing effect that will cause pain. See your doctor for more advice.
Yes. Sore heels in the morning can typically be caused by plantar fasciitis which is an inflammation of the ligament to the bottom of the foot that attaches to the heel. The ligament is tight and contracted in the morning which causes pain. As the ligament loosens up the pain usually improves. There are a variety of treatment options for plantar fascitiis including stretching to cortisone injections.