[Bobby_Light]

Sounds like shin splints. The common factor in shin splints usually (not always) is overprontation of the lower extremities (a falling in toward the center line of the body) caused by glutes that don't work due to weak deep abdominal wall musculature. The glutes decelerate pronation so when they don't work (or function) you get overpronation of the lower extremities resulting in an overpronation injury such as shin splints. Because I cannot assess you this may or may not be the case, but it should offer a start point.

I would not run with pain as the body will naturally try to avoid the pain resulting in dysfunctional motor engrams or movement patterns thereby creating compensation and more dysfunction. Pain is the body's signal that something is wrong. Don't ignore it. Some people simply are not stable enough to run and must prepare the body to due so. The rule is stability before mobility or injury will result at some time.

Possibles as to why your shin splints occur -

weak "core"
overpronation
muscle imbalance/postural issues
weak anterior (front) of lower leg
weak calves, tight calves
poor movement mechanics/running form
improper footwear/arch support
weak posterior (back side of the body)

Rehabilitation -

improve core stabilization - weak core = unstable pelvis = unstable hip, knee, ankle, glutes that don't function, and overpronation

assess posture and correct imbalances (seek professional help in this matter if possible)

assess gait/running mechanics

assess footwear

stretch/foam roll - hips, IT band, hamstrings, quads, calves, hip flexors (psoas), back; improve ankle mobility and stability

strengthen the anterior tibialis (front, lower leg)

strengthen entire posterior chain (calves, hamstrings, glutes, back) - weak posterior = compensation

improve strength, stability, and flexibility at the hips to minimize compensation