There was a long suture sticking out from above and below the knee and all I could see was one other suture that needed to be clipped about midway.
What you have had is called a subcuticular stitch which means it's put in just below the surface of the skin like so
Some surgeons will use a dissolvable suture for this, others will use a non-dissolving nylon material which has to be removed. The biggest problem with this is that at the end the suture has to be perfectly straight so it slides out smoothly but if there's anything of a kink in it, it will be very difficult to remove.
Plus side is that as long as that which is showing outside the skin is trimmed off, the rest can be left without any danger to you at all. This is the self-same material that used to repair a hernia or a tendon and causes no harm left inside.
I had the same thing happen when I had a lump removed from my forearm though it that case, the surgeon had tethered it with a small knot (which sounds very like yours too) and when the nurse cut the knot one end, she cut it right off! So she tried the other end and did exactly the same thing! However, I wasn't bothered because, as I said before, this nylon suture is quite safe left inside us. But eventually, about 3 weeks later, one end extrude from the healed wound and I was able to grab it will a tweezer and it slid out fine. This could very well happen to you too. Funny things these subcutic sutures!
I noticed my knee was really warm! It's not red at all. Just very warm. Hoping this is normal. It happened during my last PT appointment also.
It's normal in that it's a sign of a grossly overworked knee. Obviously I don't know the detail but it sounds to me like your PT is having you do far too much.