I know that it is not in your head!
And no, I would not stop exercising.
The two most common reasons for clicking in the knee are arthritis and patellofemoral syndrome. But the noises or clicking of the knee do not necessarily indicate that there is significant underlying problems with the knee.
If there is not any tenderness to touch, enlargement of the bones (protrusion of the bones) of the knees or morning stiffness, I do not think at your age that you have arthritis.
If you notice a snapping and burning pain on the outside of the knee you could have a tight iliotibial band (which is a band of tissue that runs down the outer thigh to the knee). It is almost exclusive to runners.
Here is information for you about patellofemoral pain syndrome, another cause of clicking and pain. There are exercises to do that may help if this seems like it is what is causing the discomfort.
I think it is fine to exercise--running is not the best for knees in general. If you start to have swelling or increased pain, have it checked out.
I hope this is helpful for you. If you have any more questions, let me know.