The description of your pain does sound like a tight hamstring issue. It could be either the semimembranosus (which is the hamstring muscle most medial on the back of your leg and inserts down in the back of your knee); it could be the semitendinosus (which is JUST lateral to the semimembranosus and also inserts in the back/inside part of your knee). However, it could also be a combination of the two. Chances are if one muscle is tight, the others are affected.
ALSO, you have to remember that in almost any case involving a dynamic exercise, such as running, no muscle is going to work solely by itself. If one muscle is tight, chances are an opposing muscle that aids in returning the limb to it's original position may also need attention. An example of an antagonist muscle pair would be the biceps/triceps: during a bicep curl, the bicep is contracting(shortening) and the tricep is relaxing.
SO, you may want to also do some foam rolling on the front of your quads and also in your groin. When you are stretching, the more gentle the better. I would lay off the static stretching and focus more on holding a stretch for 2-3 seconds then relaxing for 2-3 seconds then holding it again. Try to stay away from holding a continuous stretch for a long period.
Also, one good thing to remember is not only do your hamstring muscles insert down near your knee joint, they ORIGINATE up near the bottom of your gluteal muscles. The semimembranosus originates around the itial tuberosity. Another good place to gently foam roll and stretch would be your glutes.
It might seem like a lot of areas to target for one specific muscle, but you would be surprised by what a few days of regular maintanance and attention to neglected muscles can do for you.
ALSO (sorry for this being so long), a lot of times when runners come back from a break from running, they are used to having their hamstrings contracted and their glutes relaxed. This is due from longer periods of time being innactive (such as sitting). When you go to use your muscles at full force again, they don't always agree to the demand. The glutes are not firing at an optimal level, and the hamstrings tend to take over. Another simple exercise you may want to add into your stretching routine is glute bridges. However, do the exercise in the following way:
1. Lay on your back with your knees bent and your feet flat on the floor.
2. Next, push your heels slightly into the ground and lift your toes off the floor.
3. Push up into a glute bridge and focus on pushing through your heels and contracting your glutes at the same time. Keep your pelvis and hips as alligned as possible.
4. Hold the contraction for 2-3 seconds and the slowly lower your body to the floor.
Doing the exercise this way instead of just pushing with your feet flat will ensure that you are engaging your glutes and not relying on your hamstrings (which you don't want). By stimulating your glutes in this manner (say 2-3 sets of 15-20 reps a day) you will teach your body to keep them better activated for running.
Hope this helps...