Diagnosed by what kind of medical doctor?

That depends on the extent of the degeneration, the type of exercise,
the location (there's a lot of cartilage in the knee) of the damage, etc
etc etc. Generally, if it hurts, don't do it. You've found that you're
still able to exercise every other day and this is a good thing and
important in most cases for slowing degeneration. What's the issue?

Running is for healthy joints, and it's good for healthy joints. Your
joints are no longer healthy: find a different activity. And no, it
wouldn't always hurt as soon as you start to run - inflamation from
tissue damage can take a while to present itself.

I have similar knee problems and find that the pain is extremely intermittent.
Some days none at all, others it's very sharp.  The degeneration is extremely
mild, but it's still painful.   I exercise daily, although i no longer run or
walk long distances like i used to.  The things recommended to me were cycling
on a stationary bike with the resistance set low, swimming (or at least
kicking around gently in the water), and some specific quad-building exercises
with flexible bands.  I don't know if these things help or not, the pain comes
and goes the same, but hopefully it will slow degeneration.  Also keeping
weight under control is good, and i take glucosamine (whether it helps or not,
i don't know).  I was told to avoid climbing (stairs, ladders, steep hills,
etc), squatting and kneeling.