First off, whenever I get a new pair of shoes - really, even whenever I replace cleats, since matching the outline of the old one isn't necessarily identical to the millimeter - I make sure I have the tool to adjust them accessible in a jersey pocket for the first few rides. If I know I'm going to have to dig in my seat pack for my multi-tool and put it back again - turning a three minute operation into a ten minute one - it's much less likely I'll take care of a problem right away. Don't let it go 15 miles.
When you're pedaling, pay attention to where your knees are getting torqued, and rotate your cleats accordingly. Fastening your shoes loosely will help you feel which way your feet want to track inside your shoes, also.
Also the height of your new shoes, pedals and cleats may be different from your old ones. You may need to change your seat height. Pay attention to how much your knee is bending at the top of your pedal stroke.
If it were my own knees, lateral knee pain (like, right in the notch between the bones) would mean either my foot is toed-in too much or my seat is too low. But that's my own experience, not any kind of expert opinion.