The chair height may not have anything to do with your problem. The first thing to look at is your muscle strength and joint motion. Any deficits there can cause problems. It is possible you have enough strength and motion in the knee. In that case, it may be the way your muscles contract to create movement.
Altered strategies for movement or abnormal movement patterns are often the problem behind this type of problem. When you were in pain, your legs automatically changed the way the force was distributed. You probably shifted load from the painful leg to the uninvolved side.
It is also possible to unload the painful limb by changing the way you use your muscles. For example, using more hip flexor strength when rising from a seated position reduces the demand on the knee extensor muscles. Even when the pain is gone and the strength is restored, the altered strategy may persist.
You may need some additional rehab to overcome this problem. A physical therapist can help you with a retraining program to restore normal motor movement. And this is important because altered loading patterns place extra load on the other leg. Over the long-term, you could develop arthritis in the other knee.