This happens most of the time after I hit large amounts of golf balls.
What part of my swing could be causing it?
None of us are Doctors (unless there is an orthopedic surgeon lurking). But a few of us have knee issues (I have osteoarthrisis under my knee cap). You did not describe where in the knee the pain is. First, ice is your best friend. Second stretching is also a great remedy. Lastly, without seeing your swing it is tough to see what stress you are putting on the knee.
One remedy I have used is flaring my left foot. @iacas @mvmac @james_hirshfield @sk golf have all recommended this to me early on in my Evolvr lessons. I have used it ever since and it takes a great deal of stress off the knee because I am not putting force on the outside of the knee. The knee is bending as it should. It also helps get the weight forward at impact.
To the OP, I could not tell where you were physically located. Given this crazy winter we have been having quite possibly you haven't hit balls in a while. Your knee is a complex joint with several tendons holding everything in place and being able to stretch when needed. You likely over did it with out really warming up. If you are preparing for the season you probably should have taken 50-100 swings without hitting a golf ball.
You could also do some sort Jimenenz exercise program for the knees and hips without the cigar of course