What Causes Muscle Stiffness After Walking For Long?

I am a 23 year old female, 4 foot 9 inches and 121 pounds. I am very active and walk everywhere and during the winter i play outdoor hockey for up to 8 hours a day. For the past 6 months or so i have noticed when I walk my muscles become very stiff and causes alot of pain and when I went to a local clinic they doctor said it was shin plints, but it seems to be getting worse and not really adding up to shin splints!

Basically, about 5 minutes into walking either long or short walks up hill, down hill or straight stretches my legs get so heavy , it feels like there is bricks on the back of my legs causing me to walk slowly and take breaks. It has gotten so bad that when i walk i need to sit down for a few minutes then get uo walk a few minutes and sit down again. The pain is so severe that even sometimes I start crying.

I have shared my family health history with the clinic doctor but he didnt seemed concerned at all.

But basically my family has alot of helath problems, my mother recently is in remission for breast cancer, she also has deep vein thrombosis and gets blood clots regularly. we also have kidney and heart problems that i know of. Unfortunately I dont know my father side's health problems but i was told we do have a hidden heart deffect.

Could possibly direct to me a proper diagnosis, and do you think its severe enough to go to a hospital?