After a cortisone shot, the collagen structures in that area will be structurally weakened. In your case, the ligaments. Because of this, you will want to be very careful with your loading parameters. Be very careful not to overload those structures too soon. Allow for very progressive loading.
After an injury, the first step is to retrain proprioception and balance. Simple exercises that can be done anywhere include:
-single leg balance work (progress to eyes closed)
-isometric wall squats at varying knee positions
-heel digs for hamstrings activation
-short height steps up/step downs
-quad setting/terminal knee extensions (on these, if you keep your fingers pressed in to your VMO for biofeedback, you can improve recruitment)
-various forms of bridging
Those should give you a start in the early part of the rehab. I would still highly recommend that you seek the advice of a professional trained in injury assessment/rehab before starting any strengthening program. There may be factors which would alter or impact which movements would be safe and beneficial for you.
Hope that gives you some ideas.