Knee problems can be intractable, so listen to what they tell you.
I notice in both of your reports, you've gone out on two consecutive days. Why? Sounds like you're ignoring your knees. Listen; they're telling you they need a rest.
The key is to stress your body, then rest so it can adapt.
You are at the very beginning of the adaptation process, so two days in a row are obviously too much, along with the hills. Now you are going to need some time off the bike which puts you back at square one. Some new cyclists repeat this frustrating process over and over, finally giving up and sometimes injuring themselves irreparably.
As others have noted, you need to address the biomechanical issues that are causing the problem, including cleat placement, saddle height and I'll bet you're pushing gears too big for your fitness level. What's your lowest gear?
You have guessed that your cleats are too far forward and moving them back is a start, though don't make one big move.
Refer to the bike fit page linked below (but please don't take seriously that ridiculous Grant Peterson article linked above, unless you do nothing more than ride to the shops). If you continue having problems, consider Speedplay pedals. These will give maximum float (especially X-series) and accommodate your natural gait.
This refers to the argument that broke out above. For many riders, more float alleviates the tendency for cleats to force them to assume an unnatural gait. For instance, I pedal heel in on the right. Forcing the heel out, as systems with less float do, causes me hip and knee problems, which were intractable for many years.
Think about it. Back in the old days we used to ride our leather soled shoes for a while, then mark across the quill pedal indentation and nail the cleats across the line, following our natural position.
Modern clipless systems, particularly early iterations, give no guide so it is easy to get things wrong unless you are very experienced. A couple of degrees of float and careful cleat adjustment are enough for some but I'd venture most riders need some kind of expert adjustment -- especially varus/valgus foot placement.
The final arbiter should be an experienced physio/fitter -- preferably one who knows cycling. A physio might also recommend some lateral stability exercises, such as squeezing a small football between your knees.
Good luck and happy cycling.
