I treat a lot of runners. Most come in with some sort of repetitive overuse injury. They have "pushed though" something and usually "pushed through" something after that. To say that most have big compensations would be an understatement. They have built up movement dysfunction over the months/years.
Question, do you think it's normal that you start out in pain, but "after I warm up and get a few miles in, the pain goes away."
Question, do you think it's smart that you know it hurts, but "I have to get the miles in?"
Question, do you think it's OK that it only hurts when I'm done, but by my next run it usually feels pretty good?
If you answered Yes to any of these hypothetical questions, my simple statement is this. You are destroying your body. No punches pulled. Maybe it's cartilage (that medical science can't replace), a stress fracture, tendonosis (degenerative tendon changes), osteoarthritis (something is moving to much, because something else isn't moving), something.
Train Smart, don't "gut it out." Get help, get a therapist, a coach, someone to help you get back on track.
Test yourself for asymmetrical flexibilities. Is one hamstring tighter then the other? Quadriceps? Hips? Inflexibility is one thing. Asymmetrical flexibility is a surefire way to injury.
Touching your toes isn't a hamstring stretch. Quit doing it. It's an assessment. A real flexibility test I use for runners is this. Lie on your back. Have someone bend your leg and press your thigh to your chest. Does your other leg stay still? If it does you pass. If it doesn't you have work to do or your going to be overworking. Overworking = Injury.
If you really love running. Do the work it takes to run healthy. The body is beautifully and wonderfully made. It's made to last, not wear out. Most importantly, you will never get a new one.