This sounds like a classic description of shin splints syndrome. This is an condition cause by repetitive stress to the bones of the foreleg, namely the tibia. The impact of running causing inflammation in the bone which results in diffuse leg pains, at first intermittent but without proper treatment the pain will become more constant. an important distinction is between shin splints syndrome and an acute stress fracture
in the tibia. a stress fracture will normally have more localized, sharp pain as opposed to the more diffuse achy nature of shin splints. The proper treatment of shin splints is as follows:
-RICE: rest, ice, compression and elevation. essentially, this is an overuse injury
and the most effective treatment is rest. ice, compression and elevation will help with the pain, and occasional NSAIDs (ibuprofen, aleve) may also be used for pain management. Unlike with stress fracture, which requires six weeks of rest, shin splints will normally resolve within a week or so. when you feel the pain has improved, it is reasonable to take up running again (you will not worsen the injury nor cause any permanent damage) if the pain comes back, return to the RICE regimen.
-stretching and muscle strengthening are also important components of the treatment and prevention of future shin splints. at least 5-10 minutes of dedicated stretching following your workout is recommended.
Hope this helps!