Dave's suggestion is a good one.
My knees do get a little tender when I get into OLifting, but it never gets to the point you are describing.
If you aren't going to go see a doctor, you might try doing all your OL as power versions and see if it improves. If it does, then you may have a flexibility/mobility issue that can be addressed through things like stretching, joint mobility, and foam rolling.
Always better to rule out the bad stuff first. Bilateral symptoms, to me, often mean either:
1) overdoing something, too much too soon
2) systemic issues
This doesn't sound like something you want to just "train through".