Hi, tdy36. Sorry to hear of your knee tribulations.
Recovery varies so much, but generally it takes about 4-8 weeks for the fracture itself to heal. During that time, you will progress from the immobilizer to a brace (sometimes called a ROM brace). Recovery from a broken patella actually involves more than the bone healing, however. Following your period of immobilization, you will need to rehab the knee and leg to regain ROM (range of motion) and strength. It is impossible to predict how short or how long it will take, but youth and motivation are on your side.