I'll start just by saying that doctors love X-rays and sometimes take them as the final test result. It's definitely time to ask for an MRI/CAT scan which will show them everything in the knee, not just some shady outline. The knee is an extremely complicated part of the body. If you haven't done so, ask to be referred to an orthopaedic surgeon. Mine has been a huge help.
Neuropathy typically affects the extremities - hands, feet, etc. That's not to say it couldn't affect you knees, just doesn't seem likely. Also pain is not the only symptom. Burning, tingling these are very common.
Long time runners inevitably will have knee issues. I know you said you only recently started, but the type of ground you are using could be impacting your knees and joints. Something like a treadmill is much better than hard pavement.
My husband, who's not diabetic, has bad knees. If he works out too hard or is fixing something around the house and has to be on his knees, he's always in a great deal of pain for awhile after. His issue, I'm 100% sure, is that he's significantly overweight and trying to do these things, and his weight is just too much for his knees to handle.