The stiffness in the left knee is because it is feeling overworked as you are protecting the injured right. Secondly to the overuse, the muscles of the front of the thigh, the quadriceps, is getting fatigued. When that muscles faces a challenge, sudden turning or getting up after sitting, it fails to provide the required support of the knee cap which feels like giving way.
Next Steps
start putting weight on the right leg so that the left will get rest.
Health Tips
we can do a teleconsultation if you want